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|The absolute value of x is defined as the distance from x to zero on the number line. It is always greater than or equal to zero. The absolute value of x is written as |x| . | For all real numbers x : To understand what absolute value means, read the following example. Two friends, Sally and Molly, starting from point "0", traveled a distance of 50 yards in opposite directions. If we denote the place reached by Sally by positive integer +50, then the place reached by Molly could be denoted by the negative integer -50. If we do not take the direction into consideration and try to find how far each one of them has traveled, we say that both Sally and Molly are at a distance of 50 yards from starting point "0". The absolute value of an integer is the numerical value of the integer regardless of its sign. Therefore, the absolute value of an integer is always non-negative. The absolute value of an integer on the number line is nothing but the distance of the integer from "0" irrespective of its direction. Therefore, in the above example, the distance traveled by either friend is the absolute value of 50. We use two vertical lines, one on either side of the integer to show its absolute value. Therefore, the absolute value of -50 is expressed by writing |-50|. Absolute value of -50 = |-50| = 50. In general, absolute value of an integer 'a' is defined by Directions: Write the absolute value of the given integers. Also write at least 10 examples of your own.

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|HONORS GOVERNMENT UNIT OBJECTIVES| |UNIT I: THE US CONSTITUTION| |The Framers of the Constitution sought to create a government capable of protecting liberty and preserving order. The solution they chose—one without precedent at that time—was a government based on a written constitution which combined the principles of popular consent, separation of powers, and federalism. Popular consent was most evident in the procedure for choosing members of the House of Representatives. However, popular consent was limited by the requirements that senators be elected by their state legislatures and presidents by the Electoral College. Powers were separated among branches that then had to cooperate to effect change. Thus, separation of powers was joined with a system of checks and balances. This, it was hoped, would prevent tyranny, even by a popular majority. Federalism came to mean a system in which both the national and state governments had independent authority. Allocating powers between these two levels of government and devising means to ensure that neither large nor small states would dominate the national government required the most delicate compromises at the Philadelphia convention. The Framers’ decision to protect the institution of slavery was another compromise, which presumably helped to ensure the Constitution’s ratification by states engaged in the slave trade. In the drafting of the Constitution and the struggle for its ratification, the positions people took were determined by a variety of factors. In addition to their economic interests, these included profound differences of opinion over whether the state governments or the national government would be the best protector of personal liberty. States participate actively both in determining national policy and in administering national programs. Moreover, they reserve to themselves or to localities within them important powers over such public services as schooling and law enforcement, and such important public decisions as land use. In a unitary system, these powers are exercised by the national government. How one evaluates federalism depends in large part on the value one attaches to the competing criteria of equality and participation. Federalism means that citizens living in different parts of the country will be treated differently. This applies not only to spending programs (such as welfare), but also to legal systems (where civil rights may be differentially protected or criminal sentencing may vary). Yet federalism also means that there are more opportunities to participate in the decision making. It allows people to influence what is taught in the schools, and to decide where highways and other government projects will be built. Indeed, differences in public policy—that is, unequal treatment—are largely the result of wider participation in decision making. It is difficult, perhaps even impossible, to have more of one of these values without having less of the other.From the 1930s to the present, United States politics and public policy became decidedly more nationalized, with the federal government, and especially the federal courts, imposing increasingly uniform standards on the states. These usually took the form of mandates and conditions of aid. Efforts begun in the 1960s and 1970s to reverse this trend by shifting to revenue sharing and block grants were only partially successful. In the mid-1990s, the Supreme Court began to review the doctrine of state |UNIT II: LEGISLATIVE, EXECUTIVE, and JUDICIAL| Over the last fifty years or so, Congress, especially the House, has evolved through three stages. The Congress is presently an uneasy combination of stages two and three. During the first stage, which lasted from the end of World War I until the early 1960s, the House was dominated by powerful committee chairs who controlled the agenda, decided which members would get what services for their constituents, and tended to follow the leadership of the Speaker. Newer members were expected to be seen but not heard; power and prominence came only after a long apprenticeship. Congressional staffs were small, and so members dealt with each other face to face. In dealing with other members, it helped to have a southern accent: Half of all committee chairs, in both the House and the Senate, were from the South. Not many laws were passed over their objections. The second stage emerged in the early 1970s, in part as the result of trends already under way and in part as the result of changes in procedures and organization brought about by younger, especially northern, members. (As an example of continuing trends, consider the steady growth in the number of staffers assigned to each member.) Dissatisfied with southern resistance to civil rights bills and emboldened by a sharp increase in the number of liberals who had been elected in the Johnson landslide of 1964, the House Democratic caucus adopted rules that allowed the caucus to do the following: Also, the installation of electronic voting made it easier to require recorded votes, and so there was a sharp rise in the number of times each member had to go on record. The Rules Committee was instructed to issue more rules that would allow floor amendments. At the same time, the number of southern Democrats in leadership positions began to decline, while the conservativism of the remaining ones began to lessen. Moreover, northern and southern Democrats began to vote together a bit more frequently, though the conservative Boll Weevils remained a significant—and often swing—group. These changes created a House ideally suited to serve the reelection needs of its members. Each representative could be an individual political entrepreneur, seeking publicity, claiming credit, introducing bills, holding subcommittee hearings, and assigning staffers to work on constituents’ problems. There was no need to defer to powerful party leaders or committee chairs. But because representatives in each party were becoming more ideologically similar, there was a rise in party voting. Congress became a career attractive to women and men skilled in these techniques. Their skills as members were manifest in the growth of the sophomore surge, the increase in their winning percentage during their first re-election campaign. Even junior members could now make their mark on legislation. In the House, more floor amendments were offered and passed; in the Senate, filibusters became more commonplace. Owing to multiple referrals and overlapping subcommittee jurisdictions, more members could participate in writing bills and overseeing government agencies. Lurking within the changes that defined the second stage were others, less noticed at the time, that created the beginnings of a new phase. This third stage was an effort in the House to strengthen and centralize party leadership. The Speaker acquired the power to appoint a majority of the Rules Committee members. That body, worried by the flood of floor amendments, began issuing more restrictive rules. By the mid-1980s, this had reached the point where Republicans were complaining that they were being gagged. The Speaker also got control of the Democratic Steering and Policy Committee (which assigns new members to committees) and was given the power to refer bills to several committees simultaneously. These opportunities for becoming a powerful Speaker were not noticed while Tip O’Neill (D, Massachusetts) held that post. However, Jim Wright (D, Texas), O’Neill’s successor, began to make full use of these powers shortly after he entered office. Perhaps if he had not stumbled over his ethical problems, Wright might have succeeded in becoming the policy leader of the House, setting the agenda and getting much of it adopted. The replacement of Wright by Tom Foley (D, Washington) signaled a return to a more accomodationist leadership style. The pendulum continued to swing between different leadership styles in the latter half of the 1990s. Foley’s replacement, Republican Newt Gingrich (Georgia), was a more assertive policy leader. The first sitting Speaker to be reprimanded by the House for ethics violations, Gingrich resigned from office after the 1998 elections. He was succeeded by a more moderate speaker, J. Dennis Hastert (R, Illinois). The evolution of the House remains an incomplete story. It is not yet clear whether it will remain in stage two or find some way of moving decisively into stage three. For now, it has elements of both. Meanwhile, the Senate remains as individualistic and as decentralized as ever—a place where it has always been difficult to exercise strong leadership. Congress is a collection of individual representatives from states and districts who play no role in choosing the president. They are therefore free to serve the interests of their constituents, their personal political views, and (to a limited extent) the demands of congressional leaders. In serving those interests, members of necessity rely on investigating, negotiating, and compromise, all of which may annoy voters who want Congress to be “decisive.” The unpopularity of Congress is made worse by the recent tendency of its members to become ideologically more polarized. One of the most important changes in the profile of Congressional members is the increased ability of incumbents to get re-elected. This reflects the growth of constituent service, name recognition, and the weakening of party loyalties among voters. Though its members may complain that Congress is collectively weak, to any visitor from abroad it seems extraordinarily powerful. Congress has always been jealous of its constitutional authority and independence. Three compelling events led to Congress reasserting its authority. These were the war in Vietnam, which became progressively more unpopular; the Watergate scandals, which revealed a White House illegally influencing the electoral process; and the continuance of divided government, with one party in control of the presidency and another in control of Congress. In 1973, Congress passed the War Powers Act over a presidential veto, giving it a greater voice in the use of American forces abroad. The following year, it passed the Congressional Budget and Impoundment Control Act, which denied the president the right to refuse to spend money appropriated by Congress. This act gave Congress a greater role in the budget process. Congress also passed laws to provide a legislative veto over presidential actions, especially with respect to the sale of arms abroad. Not all these steps have withstood the tests of time or of Supreme Court review, but taken together they indicate a resurgence of congressional authority. They also helped set the stage for sharper conflicts between Congress and the presidency. A president, chosen by the people and with powers derived from a written constitution, has less power than does a prime minister, even though the latter depends on the support of her or his party in parliament. The separation of powers between the executive and legislative branches, the distinguishing feature of the political system in the United States, means that the president must compete with Congress in setting policy and even in managing executive agencies. Presidential power, though still sharply limited, has grown from its constitutional origins as a result of congressional delegation, the increased importance of foreign affairs, and public expectations. But while the presidential office has more power today, the president also faces higher expectations. As a result, presidential effectiveness depends not on any general grant of authority but on the nature of the issues to be confronted and the support gained from informal sources of power. Public opinion and congressional support are extremely important. As a political scientist noted so many years ago, the president’s primary power is often the power to persuade. Though the president seemingly controls a vast executive branch apparatus, only a small proportion of executive branch personnel are presidential appointees or nominees. Even these may not be under presidential control. Moreover, public support, high at the beginning of any new presidency, usually declines as the term proceeds. Consequently, each president must conserve power (and energy and time), concentrating these scarce resources to deal with a few matters of major importance. Virtually every president since Franklin D. Roosevelt has tried to gain better control of the executive branch—by reorganizing, by appointing White House aides, by creating specialized staff agencies—but no president has been satisfied with the results. In dealing with Congress, the president may be able to rely somewhat on party loyalty. Presidents whose party controls Congress tend to have more of their proposals approved. But such loyalty is insufficient. Every president must also cajole, award favors, and threaten vetoes to influence legislation. Few presidents can count on a honeymoon. Most presidents discover that their plans are at the mercy of unexpected crises.An independent judiciary with the power of judicial review—the power to decide the constitutionality of acts of Congress, the executive branch, and state governments—can be a potent political force. The judicial branch of the United States government has developed its power from the earliest days of the nation, when Marshall and Taney put the Supreme Court at the center of the most important issues of the time. From 1787 to 1865, the Supreme Court focused on the establishment of national supremacy. From 1865 to 1937, it struggled with defining the scope of the government’s power over the economy. In the present era, it has deliberated about personal liberties. It became easier for citizens and groups to gain access to the federal courts in the mid- to late twentieth century. This is the result of judges’ willingness to consider class action suits and amicus curiae briefs and to allow fee shifting. The lobbying efforts of interest groups also had a powerful effect. At the same time, the scope of the courts’ political influence has increasingly widened as various groups and interests have acquired access to the courts, as the judges have developed a more activist stance, and as Congress has passed more laws containing vague or equivocal language. Still, the Supreme Court controls its own workload and grants certiorari to a very small percentage of appellate cases. As a result, although the Supreme Court is the pinnacle of the federal judiciary, most decisions are made by the twelve circuit courts of appeals and the ninety-four federal district courts. |UNIT III: CIVIL LIBERTIES AND CIVIL RIGHTS| |Like most issues, civil liberties problems often involve competing interests—in this case, conflicting rights or conflicting rights and duties—and groups may mobilize to argue for their interests. Like some other issues, civil liberties concerns can also arise from the successful appeals of a policy entrepreneur. These appeals have sometimes reduced liberty, as when popular fears are aroused during or just after a war or attack. Civil liberties are foundational to political beliefs and political culture in the United States. Among the most important protections are those in the First Amendment: What is “speech”? How much of it should be free? How far can the state go in aiding religion? How do we strike a balance between national security and personal expression? The zigzag course followed by the courts in judging these matters has, on balance, tended to enlarge freedom of expression. Also important has been the struggle to strike a balance between the right of society to protect itself from criminals and the right of all people to be free from unreasonable searches and coerced confessions. As with free speech cases, the courts have generally broadened the rights, this time at some expense to the police. In more recent years, though, the Supreme Court has qualified some of its exclusionary rule protections. The resolution of these issues by the courts is political in the sense that there are competing opinions about what is right or desirable. In this competition of ideas and values, federal judges, though not elected, are often sensitive to strong currents of popular opinion. When no strong national mood is discernible, the opinions of elites influence judicial thinking. At the same time, courts resolve political conflicts in a manner that differs in three important respects from the resolution of conflicts by legislators and executives. First, the relative ease with which one can enter a court facilitates challenges to accepted standards. An unpopular political or religious group may have little or no access to a legislature, but it will have substantial access to the courts. Second, judges often settle controversies about rights not simply by deciding the case at hand but by formulating a general rule to cover similar cases elsewhere. This means that the law tends to become more consistent and better known, but the rules may also be inappropriately applied. A definition of “obscenity” or “fighting words” may suit one situation, but be inadequate in another. Third, judges interpret the Constitution, whereas legislatures often consult popular preferences or personal convictions. Still, though their own beliefs influence how judges read the Constitution, its language constrains almost all of their decisions.Taken together, the desire to find and announce rules, the language of the Constitution, and the personal beliefs of judges have led to a general expansion of civil liberties. As a result, even allowing for temporary reversals and frequent redefinitions, any value that is thought to hinder freedom of expression and the rights of the accused has generally lost ground to the claims of the First, Fourth, Fifth, and Sixth Amendments Through action in the courts and in the Congress, the African American civil rights movement profoundly changed the nature of African Americans’ political participation. In particular, southern African Americans entered the political system, establishing an effective array of interest groups. Another decisive move was to mobilize northern opinion on behalf of this civil rights movement. Northerners initially viewed civil rights as an unfair contest between southern whites and southern African Americans; that perception changed when court rulings and legislative decisions applied to the north as well as the south. Then, there was northern opposition to court-ordered busing and affirmative action programs. By the time this northern reaction emerged, though, the legal and political system had undergone significant change. It was difficult, if not impossible, to limit the application of civil rights laws to the south or to use legislative means to alter federal court decisions. Courts can accomplish little without strong political allies, as revealed by the massive resistance to the early school desegregation decisions. However, they can accomplish a great deal, even in the face of adverse public opinion, when they have organized allies, as was seen in their ability to withstand anti-busing efforts. The women’s movement has somewhat paralleled the organizational and tactical aspects of the African American civil rights movement. There was a significant difference, however. The women’s movement sought to repeal or reverse laws and court rulings that, sometimes, were allegedly designed to protect (rather than to subjugate) them. The conflict between protection and liberty was sufficiently strong that it defeated efforts to ratify the Equal Rights Amendment. Abortion and affirmative action are among the most divisive civil rights issues in United States politics. From 1973 to 1989, the Supreme Court seemed committed to giving constitutional protection to all abortions within the first trimester, with some regulation allowed thereafter. Since 1989, however, the Court has approved various state restrictions on all abortions. There has been a similar shift in the Court’s view of affirmative action. Though it still approves some quota plans, it now insists that they pass strict scrutiny. This has the effect of ensuring that quotas are instituted only to correct a proven history of discrimination, that they place the burden of proof on the party alleging discrimination, and that they be limited to hirings and not extended to layoffs. Congress has modified some of these rulings through legislation. The gay rights movement has proceeded along a rather different course than the struggle for African American civil rights or the women’s movement. The gay rights movement has largely proceeded on a state-by-state basis, with mixed results. States may not ban same-sex sexual relations, but they do not have to recognize gay marriages conducted in other states. Just as the country is divided on whether gay men and women should have the same rights as their heterosexual counterparts, so policy is divided as well.

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The teaching of science offers students the ability to access a wealth of knowledge and information which will contribute to an overall understanding of how and why things work like they do. Science is able to explain the mechanics and reasons behind the daily functioning of complex systems, which range from the human body to sophisticated modern methods of transport. Children and students are able to use this knowledge to understand new concepts, make well-informed decisions and pursue new interests. Science also helps to provide tactile or visible proof of many facts we read about in books or see on the television; this helps to increase understanding and helps children and teenagers to retain that information. Many students find science extremely inspiring and interesting. Science instils a sense of intrigue and enables students to develop understanding and form questions based both on the knowledge they already have and the insight they wish to gain in the future. Students who excel in science lessons are likely to develop a strong ability to think critically. At KS3 the science National Curriculum plan is supported by Pearson’s ‘Exploring Science’ texts and resources. The relevant key science skills for each year group are delivered through topics. Exploring Science will form; - A rich and stimulating learning experience – Exploring Science: Working Scientifically Student Books present Key Stage 3 Science in the series’ own unique style – packed with extraordinary photos and incredible facts – encouraging all students to explore, and to learn - Clear learning outcomes are provided for every page spread, ensuring students understand their own learning journey - New Working Scientifically pages focus on the skills required by the National Curriculum and for progression to KS4 science follows the iGCSE topic areas for the three individual sciences. The science skills are taught through the topic areas. We believe that the science laboratory practicals and demonstrations should be the cornerstone of our science courses.

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A material defines the artistic qualities of the substance that an object is made of. In its simplest form, you can use materials to show the substance an object is made of, or to “paint” the object with different colors. Usually, the substance is represented by its surface qualities (color, shininess, reflectance, etc.) but it can also exhibit more complicated effects such as transparency, diffraction and subsurface scattering. Typical materials might be brass, skin, glass, or linen. The basic (un-textured) Blender material is uniform across each face of an object (although the various pixels of each face of the object may appear differently because of lighting effects). However, different faces of the object may use different materials (see Multiple Materials). In Blender, materials can (optionally) have associated textures. Textures describe the substance: e.g. polished brass, dirty glass or embroidered linen. The Textures chapter describes how to add textures to materials. How Materials Work¶ Before you can understand how to design effectively with materials, you must understand how simulated light and surfaces interact in Blender’s rendering engine and how material settings control those interactions. A deep understanding of the engine will help you to get the most from it. The rendered image you create with Blender is a projection of the scene onto an imaginary surface called the viewing plane. The viewing plane is analogous to the film in a traditional camera, or the rods and cones in the human eye, except that it receives simulated light, not real light. To render an image of a scene we must first determine what light from the scene is arriving at each point on the viewing plane. The best way to answer this question is to follow a straight line (the simulated light ray) backwards through that point on the viewing plane and the focal point (the location of the camera) until it hits a renderable surface in the scene, at which point we can determine what light would strike that point. The surface properties and incident light angle tells how much of that light would be reflected back along the incident viewing angle (Rendering engine basic principle). Two basic types of phenomena take place at any point on a surface when a light ray strikes it: diffusion and specular reflection. Diffusion and specular reflection are distinguished from each other mainly by the relationship between the incident light angle and the reflected light angle. The shading (or coloring) of the object during render will then take into account the base color (as modified by the diffusion and specular reflection phenomenon) and the light intensity. Using the internal ray tracer, other (more advanced) phenomena could occur. In ray-traced reflections, the point of a surface struck by a light ray will return the color of its surrounding environment, according to the rate of reflection of the material (mixing the base color and the surrounding environment’s) and the viewing angle. On the other hand, in ray-traced refractions, the point of a surface struck by a light ray will return the color of its background environment, according to the rate of transparency (mixing the base color and the background environment’s along with its optional filtering value) of the material and the optional index of refraction of the material, which will distort the viewing angle. Of course, shading of the object hit by a light ray will be about mixing all these phenomena at the same time during the rendering. The appearance of the object, when rendered, depends on many interrelated settings: - World (Ambient color, Radiosity, Ambient Occlusion) - Material settings (including ambient, emission, and every other setting on every panel in that tab) - Texture(s) and how they are mixed - Material Nodes - Viewing angle - Obstructions and transparent occlusions - Shadows from other opaque/transparent objects - Render settings - Object dimensions (SS settings are relevant to dimensions) - Object shape (refractions, Fresnel effects) Check your Render When designing materials (and textures and lighting), frequently check the rendered appearance of your scene, using your chosen render engine/shader settings. The appearance might be quite different from that shown in the texture display in the 3D panel. As stated above, the material settings usually determine the surface properties of the object. There are several ways in which materials can be set up in Blender. Generally speaking, these are not compatible. You must choose which method you are going to use for each particular object in your scene: - First, you can set the Properties in the various Material panels. - Second, you can use Nodes; a graphical nodes editor is available. - Last, you can directly set the color of object surfaces using various special effects. Strictly speaking, these are not materials at all, but they are included here because they affect the appearance of your objects. These include Vertex Painting, Wire Rendering, Volume Rendering, and Halo Rendering. The exact effect of Material settings can be affected by a number of system settings. First and foremost is the renderer used: Cycles and the Blender Renderer (aka Blender Internal or BI) require quite different illumination levels to achieve similar results, and even then the appearance of objects can be quite different. Also, the material properties settings can be affected by the texture method used (single-texture, multi-texture or GLSL). So it is recommended to always select the appropriate system settings before starting the design of materials.

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Longitude measures the angular distance of a point from the reference meridian. Today, by convention, we refer to the meridian passing through the Greenwich Observatory, in England. In the age of the great geographic discoveries, however, the zero meridian passed through the Canary Islands, formerly known as the Fortunate Islands, which, in Ptolemy's time, marked the western boundary of the known world. For centuries, measuring longitude was an intractable problem, and this caused tremendous difficulties particularly in marine navigation. After the discovery of the New World, the development of an effective method for determining longitude became an ever more urgent need. Amerigo Vespucci (1454-1512) obtained good results by observing lunar eclipses, but frequent measurement errors often caused huge human and material losses. Maritime powers promised prizes and incentives to whoever could find a practical solution. The cosmographer Reiner Gemma Frisius (1508-1555) was the first to propose the use of portable clocks that could show the time of the port of departure on board, which navigators could then compare with the time calculated on the ship using astronomical instruments. However, the mechanical clocks of that period were not accurate enough to ensure a good result. Galileo Galilei (1564-1642) improved their efficiency by applying the pendulum. He believed he could solve the longitude problem by measuring the periods and eclipses of Jupiter's satellites. The solution was not found until the eighteenth century, when John Harrison built a precision chronometer that made it possible to determine the exact time difference between the port of departure and the ship's position. Given that every hour represents one-twenty-fourth of 360°, or 15°, mariners could simply multiply the length of a degree at a given parallel, typically expressed in miles or leagues, by the number of degrees corresponding to the time difference.

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This example will show how to reverse a sequence of characters using java and apache commons. Reversing a string is a piece of logic used when determining if a phrase is a palindrome. For each snippet below, the set up method has created a String to represent a phrase of words and String to hold the characters of the phrase backwards. Straight up Java This snippet will reverse a string using StringBuffer. We will create a StringBuffer by passing in a character sequence into the constructor then calling the reverse method which causes the characters to be returned in reverse order. This snippet will show how to reverse a string using recursion. Effective Java Item 51 states beware the performance of string concatenation so be cautious when using this approach as it hasn't been tested with a large string which could lead to performance implications. Reverse string using for loop This snippet will show how reverse a String using a for loop. We will iterate over the phrase of words with a for loop in reverse order collecting each character into a StringBuffer. Using a apache commons StringUtils class we will reverse a string. The underlying implementation is using a StringBuilder and calling the reverse function.

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(Optional) Mathematics behind control This optional Step explains the basic mathematics associated with motors and their controls, justifying why, for instance, when simple control is used the actual speed is less than that desired. With no control, the motor speed varies due to hills and friction. With simple proportional control (and lower gain) the motor speed is less affected by hills/friction but the speed is lower than that desired. With better proportional control (higher gain) the speed is even less affected, and closer to what is desired. With proportional plus integral control the speed is desired and (in the simplified simulation) unaffected by the hills and friction. Let’s do some calculations to confirm the simulation. Automatic control of motor Reminder: this block diagram illustrates what is happening, in terms of the output speed O, the voltage applied to the motor V, K a constant associated with the motor and D which represents the hills/friction O = V * K - D For control, we also have the desired input, I. We compute the error E and the voltage V by: E = I - O and V = calculation based on E Numbers for no control We will put some numbers in to illustrate what is happening. For our motor: K = 0.125 Suppose we want the desired speed to be 3, then we set V to 24. So if there’s no friction or hills: O = 24 * 0.125 = 3 But suppose friction and hills mean D = 0.5 then: O = 24 * 0.124 - 0.5 = 2.5 The output speed is much less than we want. Proportional control, C = 72 Let’s first investigate so called Proportional control, where the controller output is the error multiplied by a constant (it is proportional to the error). Here C is the constant in the controller, sometimes called its gain, which we initially set to 72. If the desired input speed is 3, then for P control, E is 3 – O and V is E * C, so: V = (3 - O) * C = (3 - O) * 72 Hence, if no friction/hills: O = 0.125 * V O = (3 - O) * 72 * 0.125 = (3 - O) * 9 = 27 - 9 * O By gathering all terms associated with O on one side of the equation: O + 9 * O = 27 10 * O = 27 Dividing both sides of the equation by 10 we get: O = 2.7 Clearly the speed is less than the desired value of 3 Hills and friction Let’s again suppose that hills contribute a value of 0.5 so: O = 0.125 * V - 0.5 If C = 72, then V = 72 * (3 - O), so: O = 0.125 * 72 * (3 - O) - 0.5 = 27 - 9 * O - 0.5 = 26.5 - 9 * O Gathering all the O terms together: O + 9 * O = 10 * O = 26.5 Dividing by 10: O = 2.65 With no feedback control, the 0.5 due to hills/friction reduced the speed by 0.5 from 3 to 2.5. With feedback, without hills, the speed was 2.7. With hills/feedback the speed was reduced by a further 0.05 to 2.65. The key point is that Feedback Control has reduced the effect of hills/friction by a factor of 10 (from 0.5 to 0.05) and got the speed closer to the desired value. This is why the robot speed changes less than when there’s no control in the simulation. What happens if C = 792 We will now investigate what happens when the controller gain is increased to 792. Again, we set I to 3 and D to 0.5 O = 792 * 0.125 * (3 - O) - 0.5 = 99 * 3 - 99 * O - 0.5 = 296.5 - 99 * O Gathering terms in O O + 99 * O = 100 * O = 296.5 O = 2.965 Clearly O is much closer to the desired speed of 3 and the effect of the hills/friction value of 0.5 has been reduced to 0.005. Proportional plus Integral Control A controller where V = error * C is called proportional control because the controller output is proportional to the error. To ensure there are no errors, we want integral control. Here the controller output is constant only if its input (which is the error) is zero. In practice we often use a combination: so called Proportional + Integral control. This is shortened to P + I control. Again the speed is constant only if the error is zero. Hence the output speed equals the desired speed and the hills and friction have no noticeable effect. The so called Advanced Control in the exercise Command the Robot, in Step 3.18, is in fact P + I control. ERIC uses P + I speed control. It should be noted that in reality, there are some further complications, but that is beyond the scope of the course. © University of Reading

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- slide 1 of 3 Teachers can encourage critical thinking skills, and gifted students can develop them through in-depth class discussions. Students can pose their own questions, or teachers can ask questions where students have to do more than just recall facts. For example, if you're studying the causes of the Civil War with your fifth grade class, you could ask them a simple question like: what are the causes of the Civil War? This is a knowledge question. However, you can encourage more in-depth discussions by asking questions like: compare and contrast the reasons why the North entered into a war with the South during the U.S. Civil War; or looking at the causes of the Civil War, which ones do you think were the most crucial? When students discuss questions such as these, they will be sharing their opinions with each other after analyzing information presented in class. They will also be supporting their opinions and ideas with facts. Gifted students and students on grade level can take part equally in these types of conversations. - slide 2 of 3 Teachers can develop critical thinking skills, and gifted students can improve theirs through self-evaluation. Evaluating yourself is not an easy task, and it takes a great amount of insight to identify your own strengths and weaknesses. You can ask students to evaluate themselves after they gave a presentation, for example. Students could fill out an evaluation sheet, highlighting what they did well during the presentation and what they could improve on. Students can also be taught to evaluate each other and/or discuss their own evaluation with their peers. The focus should always be on building on each individual's strengths to improve in the academic area. Other opportunities for self-evaluation and developing critical thinking skills would be at the end of a semester, at the end of a unit of study, after taking a written test, or after a game or sport. It's important for teachers to model self-evaluation and point out its usefulness in everyday life. - slide 3 of 3 Real-Life Problem Solving Teachers can help students with critical thinking skills, and gifted students can get involved in solving real life problems to develop their critical thinking skills. For example, in the classroom, students waste a lot of paper -- they might use an entire notebook sheet of paper to do five math problems; or the classroom supply of math scratch paper is always running out because students work out one problem and then put it in the recycling bin. Teachers can present the problem to the class, and then students can brainstorm more efficient ways to use paper in the classroom. They discuss the different ideas and come up with the best solution. These class discussions often take place during a classroom meeting, and the teacher acts as a facilitator. Teachers may be targeting gifted students to develop their critical thinking skills as part of the gifted curriculum, but all students can benefit from in-depth discussions, self-evaluation, and real-life problem solving. - Duke University, "Enhancing Critical-Thinking Skills in Children: Tips for Parents"

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Concepts that originated in the Roman constitution live on in both forms of government to this day. Examples include checks and balances, the separation of powers, vetoes, filibusters, quorum requirements, term limits, impeachments, the powers of the purse, and regularly scheduled elections. Even some lesser used modern constitutional concepts, such as the bloc voting found in the electoral college of the United States, originate from ideas found in the Roman constitution. Over the years, the Roman constitution continuously evolved. By the late 5th century BC, the Constitution of the Roman Kingdom had given way to the Constitution of the Roman Republic. By 27 BC, the Constitution of the Roman Republic had transformed into the Constitution of the Roman Empire. By 300 AD, the Constitution of the Roman Empire had been reformed into the Constitution of the Late Roman Empire. The actual changes, however, were quite gradual. Together, these four constitutions formed four epochs in the continuous evolution of one master constitution. The first Roman assembly, the 'comitia curiata', was founded during the early kingdom. Its only political role was to elect new kings. Sometimes, the king would submit his decrees to it for ratification. In the early years of the Republic, the comitia curiata was the only legislative assembly with any power. Shortly after the founding of the republic, however, the comitia centuriata and the comitia tributa became the predominant elective and legislative assemblies. Most modern legislative assemblies are bodies consisting of elected representatives. Their members typically propose and debate bills. These modern assemblies use a form of representative democracy. In contrast, the assemblies of the Roman Republic used a form of direct democracy. The Roman assemblies were bodies of ordinary citizens, rather than elected representatives. In this regard, bills voted on (called plebiscites) were similar to modern popular referenda. Unlike many modern assemblies, Roman assemblies were not bicameral. That is to say that bills did not have to pass both major assemblies in order to be enacted into law. In addition, no other branch had to ratify a bill (rogatio) in order for it to become law (lex). Members also had no authority to introduce bills for consideration; only executive magistrates could introduce new bills. This arrangement is also similar to what is found in many modern countries. Usually, ordinary citizens cannot propose new laws for their enactment by a popular election. Unlike many modern assemblies, in the early Republic, the Roman assemblies also had judicial functions. After the founding of the empire, the vast majority of the powers of the assemblies were transferred to the Senate. When the Senate elected magistrates, the results of those elections would be read to the assemblies. Occasionally, the emperor would submit laws to the comitia tributa for ratification. The assemblies ratified laws up until the reign of the emperor Domitian. After this point, the assemblies simply served as vehicles through which citizens would organize. The Roman senate was the most permanent of all of Rome's political institutions. It was probably founded before the first king of Rome ascended the throne. It survived the fall of the Roman Kingdom in the late 5th century BC, the fall of the Roman Republic in 27 BC, and the fall of the Roman Empire in 476 AD. It was, in contrast to many modern institutions named 'Senate', not a legislative body, but rather, an advisory one.

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Lesson 3: Ways We Communicate (Part 1) 1. Lesson Overview Length of Lesson - 60 mins Prior Knowledge (What should the Teacher Have Already Covered) - Lesson 1 on feelings. - Lesson 2 on similarities and differences - Poster of images for activity 1 or use IWB to display on screen. - Selection of resources that demonstrate different ways of communicating (*see activity 2). - Everyone benefits from being able to communicate with the people around them. - There are many ways we can communicate our thoughts and feelings. - We need to recognise the communication needs of the people around us so that we can find the best way to communicate with them. - LO1: With visual reference for support, students can identify different ways to communicate. - LO2: Students can identify a variety of ways we can communicate in the school environment (e.g. with words, emotion, pictures, sound, colour, touch). - LO3: Students can suggest appropriate inclusive activities that respond to the needs of others. 2. Australian Curriculum Links HPE Subject Area - ACPPS004: Practice personal and social skills to interact positively with others General Capabilities by the End of Foundation Year (Level 1) Personal and Social Capability - Develop self-discipline and set goals: follow class routines to assist learning - Work collaboratively: share experiences of cooperation in play and group activities - Understand relationships: explore relationships through play and group experiences - Make decisions: identify options when making decisions to meet their needs and the needs of others - Examine values: identify values that are important to them - Reflect on ethical action: identify and describe the influence of factors such as wants and needs on people’s actions - Communicate across cultures: recognise that people use different languages to communicate - Understand learning area vocabulary: use familiar vocabulary contexts related to everyday experiences, personal interests and topics taught at school and used in other contexts - Interpret and analyse learning area texts: interpret simple texts using comprehension strategies Critical and Creative Thinking - Identify and clarify information and ideas: identify and describe familiar information and ideas during a discussion or investigation. Assessable moments: As students undertake the learning experiences described in the lesson, take note of a range of assessable moments to provide information about student achievement. Ongoing assessment will provide evidence of the extent to which students achieve the identified Australian Curriculum links. Assessable moments are linked to learning outcomes and are identified by the following identifier: LO (insert number) 3. Lesson Plan: Suggested Sequence of Learning Experiences |Format||Lesson Plan: Suggested Sequence of Learning Experiences| Welcoming activity: see lesson 1 State the learning intention: Today we are going to learn about the importance of being able to let others know what we are thinking and how we are feeling, and also understand other people's thoughts and feelings. This is called communication. We will be exploring different ways to communicate, and will look at how we communicate at school. |Body 20 mins| Activity 1: Everyone can Communicate! LO1 Class Discussion: There are many ways we can communicate, or send and receive messages. Why is it important for people to be able to communicate? (to find things out, to show or how we are feeling, to say what we are thinking). How am I communicating with you now? (I am talking, you are listening). Is this the only way we can communicate, or give someone information? (no). How else can we communicate a message, or give information to someone? (assess what the students already know and develop further understanding throughout the lesson) In the first lesson, we did an activity where we communicated our feelings without using words (feelings role play activity). We used our faces and body to communicate different feelings like happiness and sadness. Show lesson 3 “Ways we communicate” table using an electronic whiteboard. Go through the table and ask students to identify the different ways of communicating by referring to the table. Ask focus questions like: Optional – print out the communication table and put it somewhere in the room for referral. Main points to highlight: Activity 2: Treasure Hunt!! Teacher’s notes: for this activity, you can use examples from your school environment and direct students to identify different types of communication. For example, communication through words, signs, pictures, sounds (school bell) and colour – e.g. your classroom, library, toilets, car park, school hall etc. LO2 Select some story books, print materials (e.g. posters, charts, procedures, diagrams), electronic media (e.g. electronic white board), music, colour etc. that show different methods of communicating in the school environment – and get students to find/ describe/ locate where they are – one at a time. Describe the activity as a communication “treasure hunt”. Once they have found the communication ‘treasure’ in the school setting, ask them to tell you when you would use this type of communication. For example (things to find): Activity 3: Playing Together without Words! Students respond to the following scenario: Display pictures of emotions on the IWB or on a poster for reference when implementing the following activity. A new girl called Sherri joins our class. She is from another country that speaks a different language. Sherri does not yet understand English. How can we communicate with Sherri to make her feel welcome? (Smile at her, use signs and pictures, show her where things are like the toilets, sit with her and find an activity that she can join in with – for example – completing a jigsaw or drawing a picture). How do we know if Sherri understands? (Expected responses: She may nod, she may look happy and relaxed, and she may join in with the activity). LO3 Class brainstorm: What activities could you do with Sherri that does not require you to understand each other’s spoken language? Choose an activity from the ones provided and complete the activity with your partner without using words. Main point to highlight: | Conclusion and Reflection| LO2, LO3 Class discussion. What are some different ways we can communicate with each other? Why is it important to find different ways of communicating?

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If statements are control flow statements which helps us to run a particular code only when a certain condition is satisfied. For example, you want to print a message on the screen only when a condition is true then you can use if statement to accomplish this in programming. In this guide, we will learn how to use if statements in Python programming with the help of examples. There are other control flow statements available in Python such as if..else, if..elif..else, nested if etc. However in this guide, we will only cover the if statements, other control statements are covered in separate tutorials. Syntax of If statement in Python The syntax of if statement in Python is pretty simple. if condition: block_of_code If statement flow diagram Python – If statement Example flag = True if flag==True: print("Welcome") print("To") print("BeginnersBook.com") Welcome To BeginnersBook.com In the above example we are checking the value of flag variable and if the value is True then we are executing few print statements. The important point to note here is that even if we do not compare the value of flag with the ‘True’ and simply put ‘flag’ in place of condition, the code would run just fine so the better way to write the above code would be: flag = True if flag: print("Welcome") print("To") print("BeginnersBook.com") By seeing this we can understand how if statement works. The output of the condition would either be true or false. If the outcome of condition is true then the statements inside body of ‘if’ executes, however if the outcome of condition is false then the statements inside ‘if’ are skipped. Lets take another example to understand this: flag = False if flag: print("You Guys") print("are") print("Awesome") The output of this code is none, it does not print anything because the outcome of condition is ‘false’. Python if example without boolean variables In the above examples, we have used the boolean variables in place of conditions. However we can use any variables in our conditions. For example: num = 100 if num < 200: print("num is less than 200") num is less than 200

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An example of typecasting is converting an integer to a string. This might be done in order to compare two numbers, when one number is saved as a string and the other is an integer. For example, a mail program might compare the first part of a street address with an integer. If the integer "123" is compared with the string "123" the result might be false. If the integer is first converted to a string, then compared with the number in the street address, it will return true. Another common typecast is converting a floating point number to an integer. This might be used to perform calculations more efficiently when the decimal precision is unnecessary. However, it is important to note that when typecasting a floating point number to an integer, many programming languages simply truncate the decimal value. This is demonstrated in the C++ function below. int float_to_int(float a) // example: a = 2.75 int b = (int)a; // typecast float to int return b; // returns 2 In order to round to the nearest value, adding 0.5 to the floating point number and then typecasting it to an integer will produce an accurate result. For example, in the function below, both 2.75 and 3.25 will get rounded to 3. int round_float_to_int(float a) // example: a = 2.75 int b = (int)(a+0.5); // typecast float to int after adding 0.5 return b; // returns 3 While most high-level programming languages support typecasting, each language uses its own method to convert data. Therefore, it is important to understand how the language converts between data types when typecasting variables. Updated: January 7, 2016

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Students observe how frictional forces are different for stationary and moving objects and determine the various factors affecting the force of friction. After completing this tutorial, you will be able to complete the following: Friction can be felt in the action of tires on pavement, the strength required to drag a heavy file cabinet, and the warmth produced by rubbing hands together. Friction is defined as a force that resists the motion of objects against each other, when the surfaces of those objects are in contact. The force of friction always acts parallel to the contact surface and opposite the applied force. When a force is applied against an object resting on a surface below a certain threshold, no motion will result. The opposing force balances the applied force and is consistent with Newton's third law of motion. The magnitude of this frictional force must equal the applied force, up to a maximum above which the friction is overcome and motion ensues. The greatest frictional force that successfully opposes the applied force (i.e., the maximum force that can be applied without moving the object) is referred to as the maximum force of static friction. Static friction acts on objects at rest. If, once in motion, a force of the same magnitude were continuously applied to the object, acceleration would result. This is because the applied force exceeds the force of friction acting on the moving object. This type of friction is known as kinetic friction, and is smaller in magnitude than static friction. Applying a force that exactly opposes kinetic friction results in a constant velocity. Friction is directly proportional to the coefficient of friction between two surfaces, as well as the object's mass, because normal force presses the two surfaces together. Friction does not, however, depend on the surface area of an object. |Approximate Time||20 Minutes| |Pre-requisite Concepts||Students should be familiar with the concept of force and how to measure force.| |Type of Tutorial||Concept Development| |Key Vocabulary||coefficient, dynamic friction, force|

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Since the early 1800's, many laws in both North and South discriminated systematically against free Blacks. In the South, "slave codes" placed significant restrictions on Black Americans who were not themselves slaves. A major purpose of these laws was maintenance of the system of white supremacy that made slavery possible. With legal prohibitions of slavery ordered by the Emancipation Proclamation, acts of state legislature, and eventually the Thirteenth Amendment, Southern states adopted new laws to regulate Black life. Although these laws had different official titles, they were (and are) commonly known as Black Codes. (The term originated from "negro leaders and the Republican organs" according to Confederate historian John S. Reynolds.) The defining feature of the Black Codes was vagrancy law which allowed local authorities to arrest the freedpeople and commit them to involuntary labor. BackgroundVagrancy laws date back to the end of feudalism in Europe. Introduced by aristocratic and landowning classes, they had the dual purpose of restricting access of "undesirable" classes to public spaces and of ensuring a labor pool as serfs became emancipated from their land. Slave codes“Slave codes” in the antebellum South contained more regulations of free Blacks than of slaves themselves. Chattel slaves basically lived under the complete control of their owners; non-slaves presented more of a challenge to the boundaries of White-dominated society. Black Codes in the antebellum South heavily regulated what people could do. Blacks could not assemble, bear arms, become literate, speak freely, or testify against White people in Court. These regulations intensified during the 1800s, intensifying after Nat Turner's insurrection of 1831, and culminating in the Supreme Court's Dred Scott decision of 1857. Restrictions on manumission and freedom of movement placed tighter and tigher restrictions on what Black people could do. These codes contained a few protections, such as prohibition against murdering slaves. Louisiana based its laws on the French Code Noir issued in 1685. As the abolitionist movement gained force and escape programs for slaves such as the Underground Railroad expanded, concern about blacks heightened among some whites in the North. North of the Mason–Dixon line, anti-Black laws were generally less severe. Some public spaces were segregated, and Blacks generally did not have the right to vote. All the slave states passed laws banning the marriage of whites and black people, so-called anti-miscegenation laws, as did several new free states, including Indiana, Illinois and Michigan. Indiana and Illinois shared borders with slave states and the southern populations of these states had cultures that shared more values with the South across the Ohio River than the northern populations. In several states the Black Codes were either incorporated into or required by their state constitutions, many of which were rewritten in the 1840s. Article 13 of Indiana's 1851 Constitution stated "No Negro or Mulatto shall come into, or settle in, the State, after the adoption of this Constitution." The 1848 Constitution of Illinois led to one of the harshest Black Code systems in the nation until the Civil War. The Illinois Black Code of 1853 prohibited any Black persons from outside of the state from staying in the state for more than ten days, subjecting Black persons who remain beyond the ten days to arrest, detention, a $50 fine, or deportation. Maryland passed vagrancy and apprentice laws, and required Blacks to obtain licenses from Whites before doing business. It prohibited Black immigration until 1865. Most of the Maryland Black Code was repealed in the Constitution of 1867, although Black women were not allowed to testify against White men with whom they had produced children. In some States, Black Code legislation used text directly from the slave codes, simply substituting Negro or other words in place of slave. Union occupationThe Union Army relied on the labor of newly freed people, and did not always treat them fairly. Thomas W. Knox wrote: "The difference between working for nothing as a slave, and working for the same wages under the Yankees, was not always perceptible." At the same time, military officials resisted local attempts to apply pre-war laws to the freed people. After the Emancipation Proclamation, the Army was able to conscript Black "vagrants" and sometimes others. The Union wage system also went into large-scale effect after the Emancipation Proclamation, upgrading free Blacks from "contraband" status. It began in February 1863 under the jurisdiction of General Nathaniel P. Banks in Louisiana. General Lorenzo Thomas implemented a similar system in Mississippi. The Banks-Thomas system offered Blacks $10 a month, with an agreement to provide rations, clothing, and medicine. The worker would have to agree to an unbreakable one-year contract. In 1864, Thomas expanded the system to Tennessee, and allowed white landowners near the Nashville contraband camp to rent the labor of refugees. Against opposition from within the Republican Party, Lincoln accepted this system as a step on the path to gradual emancipation. Abolitionists continued to criticize the system. Wendell Phillips said that Lincoln's proclamation had "free[d] the slave, but ignore[d] the Negro," calling the Banks-Thomas contracts tantamount to serfdom. The Worcester Spy described the government's answer to slavery as "something worse than failure." As the war ended, the Army implemented Black Codes to regulate the behavior of Black people in general society. Although the Freedmen's Bureau had a mandate to protect Blacks from a hostile Southern environment, it also sought to keep Blacks in their place as laborers under a system of white supremacy. The Freedmen's Bureau cooperated with Southern authorities in rounding up Black "vagrants" and placing them in contract work. In some places, it supported owners to maintain control of young slaves as apprentices. After the WarSoon after the end of slavery, white planters encountered a labor shortage and sought a way to manage it. Although Blacks did not all abruptly stop working, they did try to work less. In particular, many sought to reduce their Saturday work hours, and women wanted to spend more time on child care. In the view of one contemporary economist, freedpeople exhibited this “noncapitalist behavior” because the condition of being owned had "shielded the slaves from the market economy" and they were therefore unable to perform "careful calculation of economic opportunities." An alternative explanation treats the labor slowdown as a form of gaining leverage through collective action. And at the same time, freedpeople certainly did not want to work the long hours that had been forced upon them for their whole lives. Whatever its causes, the sudden reduction of available labor posed a challenge the Southern economy, which had relied upon intense physical labor to profitably harvest cash crops, particularly King Cotton. Southern Whites also perceived Black vagrancy as a sudden and dangerous social problem. White Americans, particularly in the South, had established their beliefs about Black people during multiple generations of living in a racist society. Whites believed that both that Black people were destined for servitude and that they would not work unless physically compelled. Culturally, free Blacks no longer felt compelled to show conspicuous deference to White people. The racial divisions which slavery had created immediately became more obvious. Blacks also bore the brunt of Southern anger over defeat in the War. Legislation on the status of freedpeople was often mandated by constitutional conventions held in 1865. Mississippi, South Carolina, and Georgia all included language in their new state constitutions which instructed the legislature to "guard them and the State against any evils that may arise from their sudden emancipation." The Florida convention of October 1865 included a vagrancy ordinance that was in effect until process Black Codes could be passed through the regular legislative process. Legislation in Southern statesBlack Codes restricted black people's right to own property, conduct business, buy and lease land, and move freely through public spaces. A central element of the Black Codes were vagrancy laws, in which states classified not working as criminal behavior. Failure to pay a certain tax, or to comply with other laws, could also be construed as vagrancy. Nine states updated their vagrancy laws in 1865–1866. Of these, eight allowed convicting leasing (a system in which state prison hired out convicts for labor) and five allowed prisoner labor for public works projects. Another important part of the Codes were the annual labor contracts, which Black people had to present in order to avoid vagrancy charges. Strict punishments against theft also served to ensnare many people in the legal system. Previously, Blacks had been part of the domestic economy on a plantation, and were more or less able to use supplies that were available. After emancipation, the same act performed by someone working the same land might be labeled as theft, leading to arrest and involuntary labor. Some states explicitly curtailed Black people's right to bear arms, justifying these laws with claims of imminent insurrection. In Mississippi and Alabama, these laws were enforced through the creation of special militias. Samuel McCall commented in 1899 that the Black Codes had "established a condition but little better than that of slavery, and in one important respect far worse": by severing the property relationship, they had diminished the incentive for property owners to ensure the relative health and survival of their workers. Regarding the question of how intentionally Southern legislatures intended to maintain White supremacy, Beverly Forehand writes: "This decision was not a conscious one on the part of white legislators. It was simply an accepted conclusion." The new laws established some positive rights for Blacks. States legalized Black marriages and in some cases increased rights to own property and conduct commerce. Mississippi was the first state to pass Black Codes. Its laws served as a model for those passed by other states, beginning with South Carolina, Alabama, and Louisiana in 1865, and continuing with Florida, Virginia, Georgia, North Carolina, Texas, Tennessee, and Arkansas at the beginning of 1866. Intense Northern reaction against the Mississippi and South Carolina laws led some of the following states to excise overt racial discrimination; nevertheless, their laws on vagracy, apprenticeship, and other topics were crafted to effect a similarly racist regime. Even states that carefully eliminated most of the overt discrimination in their Black Codes retained laws authorizing harsher sentences for Black people. MississippiMississippi was the first state to legislate a new Black Code after the war, beginning with "An Act to confer Civil Rights on Freedmen." This law allowed Blacks to rent land only within cities—effectively preventing them from earning money through independent farming. It required Blacks to present, each January, written proof of employment. The law defined violation as vagrancy, punishable by arrest—for which the arresting officer would be paid $5, taken from the arrestee's wages. Provisions akin to fugitive slave laws mandated the return of runaway workers, who would lose their wages for the year. An amended version of the vagrancy law also included punishments for sympathetic whites: That all freedmen, free negroes and mulattoes in this State, over the age of eighteen years, found on the second Monday in January, 1866, or thereafter, without lawful employment or business, or found unlawfully assembling themselves together, either in the day or night time, and all white persons so assembling themselves with freedmen, free negroes or mulattoes, or usually associating with freedmen, free negroes or mulattoes, on terms of equality, or living in adultery or fornication with a freed woman, free negro or mulatto, shall be deemed vagrants, and on conviction thereof shall be fined in a sum not exceeding, in the case of a freedman, free negro, or mulatto, fifty dollars, and a white man two hundred dollars, and imprisoned, at the discretion of the court, the free negro not exceeding ten days, and the white man not exceeding six months.Whites could avoid the code's penalty by swearing a pauper's oath. In the case of blacks, however: "the duty of the sheriff of the proper county to hire out said freedman, free negro or mulatto, to any person who will, for the shortest period of service, pay said fine or forfeiture and all costs." The laws also levied a special tax on blacks (between ages 18 and 60); those who did not pay could be arrested for vagrancy. Another law allowed the state to take custody of children whose parents could or would not support them; these children would then be "apprenticed" to their former owners. Masters could discipline these apprentices with corporal punishment. They could re-capture apprentices who escaped and threaten them with prison if they resisted. Other laws prevented blacks from buying liquor and carrying weapons; punishment often involved "hiring out" the culprit's labor for no pay. Mississippi rejected the Thirteenth Amendment on December 5. ResponsesGeneral Oliver O. Howard, national head of the Freedmen's Bureau, declared in November 1865 that most of the Mississippi Black Code was invalid. South CarolinaThe next state to pass Black Codes was South Carolina, which had on November 13 ratified the Thirteenth Amendment—with a qualification that Congress did not have the authority to regulate the legal status of freedmen. Newly elected governor James Lawrence Orr said that blacks must be "restrained from theft, idleness, vagrancy and crime, and taught the absolute necessity of strictly complying with their contracts for labor." South Carolina's new law on "Domestic Relations of Persons of Color" established wide-ranging rules on vagrancy resembling Mississippi's. Conviction for vagrancy allowed the state to "hire out" blacks for no pay. The law also called for a special tax on blacks (all males and unmarried females), with non-paying blacks again guilty of vagrancy. The law enabled forcible apprenticeship of children of impoverished parents, or of parents who did not convey "habits of industry and honesty." The law did not include the same punishments for Whites in dealing with fugitives. The South Carolina law created separate courts for Black people, and authorized capital punishment for crimes including theft of cotton. It created a system of licensing and written authorizations that made it difficult for Blacks to engage in normal commerce. The South Carolina Code clearly borrowed terms and concepts from the old slave codes, re-instituting a rating system of "full" or "fractional" farmhands and often referring to bosses as "masters." ResponsesA "Colored People's Convention" assembled at Zion Church in Charleston to condemn the Codes. In a memorial (petition) to Congress, the Convention expressed gratitude for emancipation and the Freedmen's Bureau, but requested (in addition to suffrage) ”that the strong arm of law and order be placed alike over the entire people of this State; that life and property be secured, and the laborer as free to sell his labor as the merchant his goods.” Some Whites, meanwhile, thought the new laws did not do enough. One planter suggested that the new laws would require paramilitary enforcement: “As for making the negroes work under the present state of affairs it seems to me a waste of time and energy […] We must have mounted Infantry that the freedmen know distinctly that they succeed the Yankees to enforce whatever regulations we can make.” Edmund Rhett (son of Robert Rhett) wrote that although South Carolina might be unable to undo abolition, “it should to the utmost extent practicable be limited, controlled, and surrounded with such safe guards, as will make the change as slight as possible both to the white man and to the negro, the planter and the workman, the capitalist and the laborer.” General Daniel Sickles, head of the Freedmen's Bureau in South Carolina, followed Howard's lead and declared the laws invalid in December 1865. Further legislationHowever, even as the legislators passed these laws, they despaired of the forthcoming response from Washington. James Hemphill said: "It will be hard to persuade the freedom shriekers that the American citizens of African descent are obtaining their rights." Orr moved to block further laws containing explicit racial discrimination. In 1866, the South Carolina code came under increasing scrutiny in the Northern press and was compared unfavorably to freedmen's laws passed in neighboring Georgia, North Carolina, and Virginia. In a special session held in September 1866, the legislature passed some new laws in concession to the rights of free Blacks. Shortly after, it rejected the Fourteenth Amendment. LouisianaThe Louisiana legislature, seeking to ensure that freedmen were “available to the agricultural interests of the state”, passed similar yearly contract laws and expanded its vagrancy laws. Its vagrancy laws did not specify Black culprits, though they did provide a “good behavior” loophole subject to plausibly racist interpretation. Louisiana passed harsher fugitive worker laws and required blacks to present dismissal paperwork to new employers. State legislation was amplified by local authorities, who ran less risk of backlash from the federal government. Opelousas, Louisiana passed a notorious code which required freedpeople to have written authorization to even enter the town. The code prevented freedpeople from living in the town or walking at night except under supervision of a White resident. Thomas Conway, the Freedmen's Bureau commissioner for Louisiana, testified in 1866: Some of the leading officers of the state down there—men who do much to form and control the opinions of the masses—instead of doing as they promised, and quietly submitting to the authority of the government, engaged in issuing slave codes and in promulgating them to their subordinates, ordering them to carry them into execution, and this to the knowledge of state officials of a higher character, the governor and others. […] These codes were simply the old black code of the state, with the word 'slave' expunged, and 'Negro' substituted. The most odious features of slavery were preserved in them.Conway describes surveying the Louisiana jails and finding large numbers of Black men who had been secretly incarcerated. These included members of the Seventy-Fourth Colored Infantry who had been arrested the day after they were discharged. The state passed an even harsher version of its code in 1866, outlawing "impudence," "swearing," and other signs of "disobedience." FloridaOf the Black Codes passed in 1866 (after the Northern reaction had become apparent), only Florida's rivaled those of Mississippi and South Carolina in severity. Florida's slaveowners seemed to hold out hope that the institution of slavery would simply be restored. Advised by the Florida governor and attorney general as well as by the Freedmen's Bureau that it could not constitutionally revoke Black people's right to bear arms, the Florida legislature refused to repeal this part of the codes. The Florida vagrancy law allowed for punishments of up to one year of labor. Children whose parents were convicted of vagrancy could be hired out as apprentices. These laws applied to any "person of color," which was defined as someone with at least one Negro great-grandparent. White women could not live with men of color. Colored workers could be punished for disrespecting White employers. Explicit racism in the law was supplemented by racist enforcement discretion (and other inequalities) in the law enforcement and legal systems. MarylandIn Maryland, a fierce battle began immediately after emancipation (by the Maryland Constitution of 1864) over apprenticeship of young black people. Former slave owners rushed to apprentice the children of freed people; the Freedmen's Bureau and some others tried to stop them. The legislature stripped Baltimore Judge Hugh Lennox Bond of his position because he cooperated with the Bureau in this matter. Salmon Chase eventually overruled the apprentice laws on the grounds of the Civil Rights Act of 1866. North CarolinaNorth Carolina's Black Code specified racial differences in punishment only for Blacks convicted of rape. TexasThe Texas Constitutional Convention met in February 1866, declined to ratify the (already effective) Thirteenth Amendment, provided that Blacks would be "protected in their rights of person and property by appropriate legislation" and guaranteed some degree of rights to testify in court. Texas modeled its laws on South Carolina's. The legislature defined Negroes as people with at least one African great-grandparent. Negroes could chose their employer, before a deadline. After they had made a contract, they were bound to it. If they quit "without cause of permission" they would lose all of their wages. Workers could be fined $1 for acts of disobedience or negligence, and 25 cents per hour for missed work. The legislature also created a system of apprenticeship (with corporal punishment) and vagrancy laws. Convict labor could be hired out or used in public works. Negroes were not allowed to vote, hold office, sit on juries, serve in local militia, carry guns on plantations, homestead, or attend public schools. Interracial marriage was banned. Rape sentencing laws stipulated either capital punishment, or life in prison, or a minimum sentence of five years. Even to commentators who favored the codes, this "wide latitude in punishment" seemed to imply a clear "anti-Negro bias." TennesseeTennessee had been occupied by the Union for a long period during the war. As military governor of Tennessee, Andrew Johnson declared a suspension of the slave code in September 1864. However, these laws were still enforced in lower courts. In 1865, Tennessee freedpeople had no legal status whatsoever, and local jurisdictions often filled the void with extremely harsh Black Codes. During that year, Blacks went from one-fiftieth to one-third of the State's prison population. Tennessee had a particularly urgent desire to re-enter the Union's good graces and end the occupation. When the Tennessee Legislature began to debate a Black Code, it received such negative attention in the Northern press that no comprehensive Code was ever established. Instead, the State legalized Black suffrage and passed a civil rights law guaranteeing Blacks equal rights in commerce and access to the Courts. However, Tennessee society, including its judicial system, retained the same racist attitudes as did other states. Although its legal code did not discriminate against Blacks so explicitly, its law enforcement and criminal justice systems relied more heavily on racist enforcement discretion to create a de facto Black Code. The State already had vagrancy and apprenticeship laws which could easily be enforced in the same way as Black Codes in other states. Vagrancy laws came into much more frequent use after the war. And just as in Mississippi, Black children were often bound in apprenticeship to their former owners. The legislature passed two laws on May 17, 1865; one to "Punish all Armed Prowlers, Guerilla, Brigands, and Highway Robbers"; the other to authorize capital punishment for thefts, burglary, and arson. These laws were targeted at Blacks and enforced disproportionately against Blacks, but did not discuss race explicitly. Tennessee law permitted Blacks to testify against Whites in 1865, but this change did not immediately take practical effect in the lower courts. Blacks could not sit on juries. Still on the books were laws specifying capital punishment for a Black man who raped a White woman. Tennessee enacted new vagrancy and enticement laws in 1875. KentuckyKentucky had established a system of leasing prison labor in 1825. This system drew a steady supply of laborers from the decisions of "negro courts," informal tribunals which included slaveowners. Free Blacks were frequently arrested and forced into labor. Kentucky did not secede from the Union and therefore gained wide leeway from the federal government during Reconstruction. With Delaware, Kentucky did not ratify the Thirteenth Amendment and maintained legally slavery until it was nationally prohibited when the Amendment went into effect in December 1865. After the Thirteenth Amendment took effect, the state was obligated to rewrite its laws. The result was a set of Black Codes passed in early 1866. These granted a set of rights: to own property, make contracts, and some other innovations. They also included new vagrancy and apprentice laws, which did not mention Blacks explicitly but were clearly directed toward them. The vagrancy law covered loitering, "rambling without a job" and "keeping a disorderly house." City jails filled up; wages dropped below pre-war rates. The Freedmen's Bureau in Kentucky was especially weak and could not mount a significant response. The Bureau attempted to cancel a racially discriminatory apprenticeship law (which stipulated that only White children learn to read) but found itself thwarted by local authorities. Some legislation also created informal, de facto discrimination against Blacks. A new law against hunting on Sundays, for example, prevented Black workers from hunting on their only day off. Kentucky law prevented Blacks from testifying against Whites, a restriction which the federal government sought to remedy by providing access to federal courts through the Civil Rights Act of 1866. Kentucky challenged the constitutionality of these courts and prevailed in Blyew v. United States (1872). All contracts required the presence of a White witness. Passage of the Fourteenth Amendment did not have a great effect on Kentucky's Black Codes. Reconstruction and Jim CrowThe Black Codes outraged public opinion in the North because it seemed the South was creating a form of quasi-slavery to negate the results of the war. When the Radical 39th Congress re-convened in December 1865, it was generally furious about the developments that had transpired during Johnson's Presidential Reconstruction. The Black Codes, along with the appointment of prominent Confederates to Congress, signified that the South had been emboldened by Johnson and intended to maintain its old political order. Railing against the Black Codes as returns to slavery in violation of the Thirteenth Amendment, Congress passed the Civil Rights Act of 1866, the Fourteenth Amendment, and the Second Freedmen's Bureau Bill. The Memphis Riots in May 1866 and the New Orleans Riot in July brought additional attention and urgency to the racial tension state-sanctioned racism permeating the South. After winning large majorities in the 1866 elections, the Republican Congress passed the Reconstruction Acts placing the South under military rule. This arrangement lasted until the military withdrawal arranged by the Compromise of 1877. In some historical periodizations, 1877 marks the beginning of the Jim Crow era. The 1865–1866 Black Codes were an overt manifestation of the system of white supremacy that continued to dominate the American South. Historians have described this system as the emergent result of a wide variety of laws and practices, conducted on all levels of jurisdiction. Because legal enforcement depended on so many different local codes, which underwent less scrutiny than statewide legislation, historians still lack a complete understanding of their full scope. It is clear, however, that even under military rule, local jurisdictions were able to continue a racist pattern of law enforcement, as long as it took place under a legal regime that was facially race-neutral. In 1893–1909 every Southern state except Tennessee passed new vagrancy laws. These laws were more severe than those passed in 1865, and used vague terms that granted wide powers to police officers enforcing the law. In wartime, Blacks might be disproportionately subjected to "work or fight" laws, which increased vagrancy penalties for those not in the military. The Supreme Court upheld racially discriminatory state laws and invalidated federal efforts to counteract them; in Plessy v. Ferguson (1896) it upheld the constitutionality of racial segregation and introduced the "separate but equal" doctrine. A general syststem of legitimized anti-Black violence, as exemplified by the Ku Klux Klan, played a major part in enforcing the practical law of white supremacy. The constant threat of violence against Black people (and White people who sympathized with them) maintained a system of extralegal terror. Although this system is now well known for prohibiting Black suffrage after the Fifteenth Amendment, it also served to enforce coercive labor relations. Violence often occurred in response to perceived affronts; sometimes it was plainly genocidal. Fear of random violence provided new support for a paternalistic relationship between plantation owners and their Black workers. Legacy and interventionsThis regime of White-dominated labor was not identified by the North as involuntary servitude until after 1900. In 1907, Attorney General Charles Joseph Bonaparte issued a report, Peonage Matters, which found that, beyond debt peonage, there was a widespread system of laws "considered to have been passed to force negro laborers to work." After creating the Civil Rights Section in 1939, the federal Department of Justice launched a wave of successful Thirteenth Amendment prosecutions against involuntary servitude in the South. Many of the Southern vagrancy laws remained on the books until the Supreme Court's Papachristou v. Jacksonville decision in 1972. Although by 1972 the laws were defended as preventing crime, the Court held that Jacksonville's vagrancy law "furnishes a convenient tool for 'harsh and discriminatory enforcement by local prosecuting officials, against particular groups deemed to merit their displeasure.'" Even after Papachristou, police activity in many parts of the U.S. discriminates against racial minority groups. Gary Stewart has identified contemporary gang injunctions—which target young Black or Latino men who gather in public—as a conspicuous legacy of Southern Black Codes. Stewart argues that these laws maintain a system of white supremacy and reflect a system of racist prejudice, even though racism is rarely acknowledged explicitly in their creation and enforcement. Contemporary Black commentators have argued that the current racially biased regime of mass incarceration, with a concommitant rise in prison labor, is comparable (perhaps unfavorably) with the historical Black Codes. Comparative historyThe desire to recuperate the labor of officially emancipated people is common among societies (most notably in Latin America) that were built on slave labor. Vagrancy laws and peonage systems are widepsread features of post-slavery societies. One theory suggests that particularly restrictive laws emerge in more larger countries, such as Jamaica and the U.S., where the ruling group does not occupy land at a high enough density to prevent the freedpeople from gaining their own. However, it seems, the U.S. was uniquely successful in maintaining involuntary servitude after legal emancipation. Historians have also compared the end of the slavery in the U.S. to the formal decolonization of Asian and African nations (many of which were subjected to slavery by their European rulers). Like emancipation, decolonization was a landmark political change—but its significance was tempered by the continuity of economic exploitation. The end of legal slavery in the U.S. did not seem to have major effects on the global economy or international relations. Given the pattern of economic continuity, writes economist Pieter Emmer, "the words emancipation and abolition must be regarded with the utmost suspicion." How did the black codes deny rights? The black codes denied rights by allowing local officials to arrest and fine unemployed African Americans and then make them work for white employers to pay off their fines. Other black codes banned African Americans from owning or renting farms. One black code allowed whites to take orphaned African American children as "unpaid apprentices". To freed men and women and many Northerners, the black codes reestablished slavery in disguise. - 40 acres and a mule - Apartheid in South Africa - Code Noir - Digges Amendment - Grandfather clause - Judicial aspects of race in the United States - List of Jim Crow law examples by State - Racial segregation in the United States - Reverse Underground Railroad - Wage slavery Text of laws - 1865 Black Codes of Mississippi - "An Act to Establish and Regulate the Domestic Relations of Persons of Color..." or the Black Codes of South Carolina, December 1865 - Black Codes in the Former Confederate States - Texas State Historical Association: Black Codes by Carl H. Moneyhon - Black codes and Jim Crow laws in South Carolina - Slavery by Another Name by Doug A. Blackmon - The Southern "Black Codes" of 1865-66 Article, Discussion Questions, and Activity from Constitutional Rights Foundation - The Illinois Black Code by Roger D. Bridges (pre-1865)

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Measuring the distance to a star makes use of astrometry – the careful monitoring of a position of a star over time. As Earth orbits the sun, it has a maximum displacement from any given position along its orbit of about 2 AU (i.e., being on the other side of the orbit). By observing the angular change in the apparent position of a star 2 AU apart, simple trigonometry can allow you to calculate the distance to the star. In the middle of the last century (not terribly long ago from a historical perspective), we knew the distances to very few stars and knew their positions with much poorer accuracy. The FK4 catalogue catalogued the position of stars in the year 1950 with a precision of position of about 0.04 arcsec in the northern hemisphere, and a dismal 0.08 arcsec precision in the southern hemisphere. It was suggested that using a network of astrolabes over ten years could reduce the errors to about 0.03 arcsec, only marginally better. Major obstacles to the advance of stellar cartography was the typical issues that plague amateur astronomers now — atmospheric distortion of stellar images, instrumental instability, and inability for a ground-based observatory to view the entire sky. In 1966, Pierre Lacroute came up with an idea (that he himself called “weird”) of performing the necessary measurements from a spacecraft, orbiting Earth outside the atmosphere. The idea was presented in 1967 to the IAU where it received a great deal of interest, but the technological capacity at the time (and available rocketry in France) was not accommodating to the idea. The satellite, a 140 kg spacecraft designed to observe 700 stars all over the sky with a precision of 0.01 arcsec, had stability requirements that could not be met by the Diamant rocket used by France at the time. The idea of a spacecraft to catalogue the distances and positions of a large number of stars evolved over time and was revised and improved for the next decade, while the rest of astrophysics advanced and continued running into the problem of distance scales being poorly known. “The determination of the extragalactic distance scale, like so many problems that occupy astronomers attention, is essentially an impossible task. The methods, the data, and the understanding are all too fragmentary at this time to allow a reliable result to be obtained. It would probably be a wise thing to stop trying for the time being and to concentrate on better establishing such things as the distance scale in our Galaxy.” — Hodge (1981) Support for a space-based astrometry mission continued to grow and recognising that France alone did not have the resources necessary to complete the task, the European Space Agency planned and devised a new spacecraft, Hipparcos, to catalogue the positions of 100,000 stars and to determine their positions with an accuracy of 0.001 arcsec (1 milliarcsec). Hipparcos was launched on August 8, 1989 on a 3.5 year mission. It determined the positions of stars, monitored the position over the course of a half year to determine the parallax and thus distance to the star, monitored the position over the course of the entire mission to determine the proper motion of the star in space, measured the spectrum of stars to determine their composition, and performed radial velocity measurements on these stars to determine their motion toward or away from Earth. In total, 118,200 stars were observed with high precision observations (published in 1997), with another 2.5 million stars observed with lower precision (published in 2000). Hipparcos data has practically revolutionised astronomy. With the knowledge of the positions and motions of over a hundred thousand stars in hand, we’ve been able to understand the structure and dynamics of nearby clusters, understand the local structure of the Galaxy, understand the orbits and true orientations of binary star systems, and more. Even an extrasolar planet transit was observed (though it was not known until the planet was discovered later). This brings us to today. This Hipparcos catalogue remains as the best available source of uniform parallaxes and positions. It is time, however, to take another step forward, with greater precision, a larger sample, and newer science. The successor to Hipparcos is called GAIA – Global Astrometric Interferometer for Astrophysics – however it will not use interferometry due to a design change. Gaia will essentially do exactly what Hipparcos did, but better. Whereas Hipparcos only measured a hundred thousand stars down to brightnesses of V = 9, Gaia will observe over a billion stars with brightnesses down to V = 20. Gaia will measure the angular position of all stars of magnitude 5.7 – 20. For stars brighter than V = 10, it will determine the position with a precision of 7 µas (microarcseconds), a precision of 12 – 25 µas down to V = 15, and 100 – 300 µas down to V = 20. It will acquire their spectrum (from 320 – 1000 nm) to determine their temperature, age, mass, and composition. It will also measure the radial velocity of stars with a precision of 1 km s-1 for V = 11.5, and 30 km s-1 for V = 17.5. Tangential velocities for 40 million stars will be measured with a precision better than 0.5 km s-1. While the stellar astrophysics enabled by Gaia will be revolutionary in its own right, the unprecedented astrometric precision also makes the mission interesting from an extrasolar planet perspective. Hipparcos was not able to discover any planets on its own, but it was marginally helpful for extrasolar planet science. Planets detected with radial velocity have unknown true masses. The greater the true mass of the planet, the greater the astrometric amplitude of the barycentric motion of the star is (see this post where astrometry is discussed in the context of planet detection). Planets of especially high true masses would therefore have a chance of having their star’s barycentric motion detectable to Hipparcos. Otherwise, Hipparcos data could be used to set upper limits to the true mass of the planet, by knowing that it’s astrometric effect must be sufficiently low so as to not have been detected by Hipparcos (an upper limit to the astrometric amplitude and thus the planetary mass). The astrometric precision and vast number of targets available to Gaia will allow for the detection of a large number of planets. Astrometry is, of course, less biased toward high values of the planetary orbital inclination, and will permit us to know the true mass of the planet and orientation of the orbit in 3D space. Still, several complications are expected to arise based on nearly two decades of radial velocity experience. Just like with radial velocity (and, actually, science in general), models will need to be fitted to data points to yield high-quality fits, however as Doppler spectroscopy has shown us, planetary systems can often feature several components all contributing to the barycentric velocity profile of the star, complicating radial velocity fitting in the same way it can be expected to complicate astrometric fitting. Radial velocity surveys can often produce more than one model that fit the data nicely, where both models may disagree on certain aspects of the orbit, or even number of planets. Astrometry is likely to be prone to the same problems. In the case of astrometry, it may even be harder because of the greater number of free parameters – ascending node, inclination, etc, issues that need to be modelled for an astrometric fit that could usually be ignored for a radial velocity fit. These challenges can be addressed and handled, and the Gaia data will be wonderfully productive to extrasolar planet science. It is hard to know how many planets we can expect Gaia to discover, because statistics for planets in intermediate-period orbits are still unconstrained, but with the accuracy and large number of stars Gaia will observe, it is likely that Gaia will discover thousands of giant planets. It will be sensitive to Jupiter analogues out to 200 parsecs. What about transiting planets? A transit of HD 209458 b was squeezed out of Hipparcos data, which was not at all optimised for transiting planet science. Can Gaia be expected to detect transiting planets? As far as photometric precision, Gaia is expected to achieve 1 mmag precision for most objects Gaia will observe, down to V ~ 15, and 10 mmag precision at the worst case of V ~ 20. For most hot Jupiter systems, mmag precision is indeed sufficient for transit detections. The next major issue is cadence. Focused transit searches tend to be high-cadence, narrow field observations, whereas Gaia is an all-sky, low cadence observatory. On average, each star will be observed by Gaia 70 times, giving us 70 measurements for a light curve of any given star with a baseline of five years. While 70 measurements spread out over five years seems dismal (and let’s not sugar-coat the issue — for a transit search, it is dismal, but Gaia is not designed to be a transit search mission), but for a planet in a short period orbit, perhaps three or four measurements may occur while the planet is transiting. Obviously, the longer the orbital period, the less a fraction of the planet’s orbital period is spent in-transit, and the fewer transits will be observed by Gaia. Since only 70 measurements will be taken, Gaia is severely biased toward short-period transiting planets. Early studies suggested wildly fantastic transiting planet yields. Høg (2002) estimated over a half million hot Jupiters and thousands of planets in longer periods would be found, based on the (unrealistic) assumption that a transit could be identified based on a single data point and other oversimplifications. Robichon (2002) suggested that Gaia will detect 4,000 – 40,000 transiting hot Jupiters under the assumption that each star would receive an average of 130 measurements, however the currently planned Gaia mission has instead 70 measurements per star. Dzigan & Zucker suggest that Gaia could potentially detect sub-Jupiter-sized planets around smaller stars, and that a ground-based follow-up campaign can easily observe hints of transiting planets that show up in Gaia data. They also suggest that a few hundred to a few thousand hot Jupiters could be found in Gaia photometry. While Gaia will perform km s-1 radial velocity measurements on millions of stars, this precision level is simply not sufficient to detect even hot Jupiters. It will, however, be able to tell if a transiting planet candidate is a brown dwarf instead, or an eclipsing binary star, allowing for one method of ruling out false positives. Interestingly, the astrometric fit to the orbit of a planet will have the inclination of the planetary orbit sufficiently well-characterised that a list of planets that are likely to transit can be compiled and followed-up with ground-based radial velocity and photometry. These long-period transiting planets will certainly prove valuable – they will be likely to host detectable rings and moons. ESA will launch Gaia on a Soyuz ST-B rocket in November of this year. It will take five years after a commissioning phase for the total extrasolar planets science results to become known. It will be very exciting to see what giant planets exist in the solar neighbourhood. They will attract interest in follow-up observations to discover smaller, inner worlds that may exist. Gaia has the potential for flagging the first solar system analogues in the solar neighbourhood for dedicated study.

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Understand decimal notation for fractions, and compare decimal fractions. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. Decimal comparisons, like fraction comparisons, are only valid if the whole is the same size. There are multiple ways to compare decimals (place value positions, visual models, estimation) just as there are multiple ways to compare whole numbers. Students may think that a decimal is the decimal point rather than a number. Students need to understand that the decimal point is a symbol that indicates the location of the ones place and all other subsequent place values in the decimal system. The decimal point separates the whole number amount from a number that is less than one. Student Knowledge Goals I know comparisons are valid when the two decimals refer to the same whole. I can justify conclusions about the comparison of decimals using visual models and other methods. I can relate a decimal to a whole number. I can use what I know about fractions to help me compare decimals. comparison symbols (<, >, =) visual models for decimals (grid paper, number line, base ten blocks etc.) Engage NY Module 6 C-9 – Use the place value chart and metric measurement to compare decimals and answer comparison questions. Engage NY Module 6 C-10 – Use area models and the number line to compare decimal numbers, and record comparisons using <, >, and =. Engage NY Module 6 C-11 – Compare and order mixed numbers in various forms. Engage NY Module 6 D-12 – Apply understanding of fraction equivalence to add tenths and hundredths. Engage NY Module 6 D-13 – Add decimal numbers by converting to fraction form. Online Problems and Assessments Khan Academy – Questions and Video Lessons Compare money amounts Compare decimals on number lines Compare decimal numbers Put decimal numbers in order Put tricky decimals in order Compare fractions and decimals on number lines

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Learn what the Math Building Blocks representation is and how to use it in the classroom. Become familiar with the strengths and limitations of the model. Use colored blocks to visualize prime factorizations. Explore beautiful patterns. Reason about relationships. Solve challenging puzzles. Visualize properties of multiplication, division and exponents. Understand why they make sense. Visualize factors easily. Discover new ways to find them. Create a formula for counting them. Develop new strategies for finding GCFs and LCMs. Discover and visualize a powerful relationship between the GCF and LCM. Discover connections between exponents and radicals. Use prime factorizations to recognize and work with with powers and roots. Use properties of exponents and radicals to name expressions in many equivalent ways. Use "anti-blocks" to represent reciprocals and fractions. Make connections to addition and subtraction. Explore properties of reciprocals. Use the Math Building Blocks to discover and apply rules for simplifying, multiplying, and dividing fractions. Use the Math Building Blocks to represent variables in order to generalize concepts from the first seven chapters. Use the Math Building Blocks recognize, explore, and analyze parallels between objects and properties belonging to the worlds of addition and multiplication. (currently being written) Synthesize and extend learning from chapters 5 through 9. (currently being written) Use the Math Building Blocks to explore abstract properties of divisibility and to visualize famous proofs such as the infinitude of primes and the irrationality of the square root of 2. (currently being written) Learn about alternate ways to introduce the Math Building Blocks to students. Download a version of the building blocks grid that uses symbols instead of colors. Watch slide shows that use the blocks to illustrate a modified version of the Sieve of Eratosthenes. Play a prime factorization game on the computer. Explore a huge prime factorization grid that shows the block diagrams for all natural numbers from 1 through 1024.

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Let's Play Ball Students will be able to collect data and plot fractions on a line plot. - Tell students that today they will be playing a game to learn a new math skill. - Tell them that they will use information from their game, or the game's data, to make a type of graph where the frequency of an item is recorded along a number line called a line plot. - Explain to students that they will be making a data chart, which is used to organize the data, and a line plot, which shows data on a number line to show frequency. Explicit Instruction/Teacher Modeling(15 minutes) - Demonstrate how to create a data chart. Give students an example problem. Example: A group of 5 students are supposed to read 8 books over the summer. - Tell students that you're going to make a data chart to show how to record the information from about the students. - Draw a data chart where the left column is labeled "students" and the right column is labeled "books read." - Explain that you will record the number of books read as a fraction out of eight. - Tell students that the numerator is the part, or number of books the students have read, and the denominator represents the total of the set, which in this case is eight for the total number of books. - Fill in the chart with your own data. Explain that when a fraction is 3/8, it means that a student read three out of the recommended eight books. - Explain that with this data we can create a line plot to show frequency, or the number of times a certain outcome occurs. - Draw a line plot and show with Xs and fractions where the data would be placed. - Ask students to find the most frequented number of books read. Guided Practice/Interactive Modeling(15 minutes) - Explain to the students that they are going to play a game of silent ball. Let them know that after they are put into groups they must make a data chart. - On the left side they need to label the column "Students" and write the names of each person in the group. - Have students label the right column "number of catches." - Each student will be given 6 chances to catch the "silent" ball. Tell students that it is called the silent ball because there is no talking. - Ask the students what they think the denominator should be. They should answer "six." - Tell your students to create the line plot. Taking data from various groups, brainstorm what fractions should be used on the graph. - Place the students in groups. Independent Working Time(15 minutes) - Tell the students that after each person's turn they should place the data next to there name on the data chart. * Tell them to make sure that they record all the data before plotting it on the line plot. - Monitor their work as they are recording their data on the chart. - Enrichment: Students that are more advanced can find the range, mode, and average of the data. They can also complete the Skiing Time Averages worksheet. - Support: Match students that need extra support with a peer to help them correctly record the data. - Have the students plot data on a data chart and plot it on a blank line plot. Check for correct placements of fractions and Xs on the line plot. Review and Closing(5 minutes) - Ask students why data charts and line plots are useful in the real world. - Ask students to brainstorm what other games use data to record information, and what the relevance of this information is.

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Grade(s): Preschool, Lower Elementary, Upper Elementary 1. Students will be able to identify cooking areas of the home that should be “Kid-free” to avoid danger from fire or injuries. 2. Students will be able to implement a plan for their own homes that feature “Kid-Free Cooking Zones” for safety. 1. Activity Sheet – Kitchen 2. Crayons or Markers 1. Ask students if they know what a fire hazard is and where some might be in their home. a. Students should identify the following: electrical appliances, electrical cords, matches & lighters, Fireplaces, materials on lamps, grills, kitchens, pot holders or paper towels left on stove, etc. 2. Explain to students that most fires start in the kitchen and it is because people don’t pay enough attention when they are cooking. 3. Ask students how they can help prevent fire and injuries while their parent or guardian is working in the kitchen. a. Responses will vary based on the age of students. b. Help watch younger children, stay out of the kitchen, only help if asked to, keep an eye on pots, don’t touch anything without permission, etc. c. The most important way to help is the focus of the lesson- Have a “Kid-Free” Cooking Zone in the kitchen and by the grill. 4. Distribute the Kitchen Activity sheet. Explain that there should be a 3 ft. “Kid-Free Cooking Zone” away from the stove. Have students trace the outlined zone on the sheet. 5. Have students identify other fire and injury hazards on the activity sheet. a. Younger Students: You may want to enlarge the activity sheet or project it on the screen and talk through the dangers as a whole class, while students circle/color their own sheets. b. Older Students: Have students work independently or in small groups to identify the hazards on the activity sheet. Discuss as a whole group the dangers in the picture. 6. Be sure students take home the completed Activity Sheet(s) so they can discuss what they learned with their families. Kitchen Safety Activity Sheet Kitchen Safety Activity Sheet Answer Key

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People in the United States have not melted into one homogeneous group. Ethnic groups have retained customs, language, and beliefs. Some have referred to this special diversity as the "tossed salad" effect. Diversity in our population is likely to remain. In 1987, immigrants from 48 different countries arrived on U.S. shores. Our country's Hispanic population increased 30 percent in the last decade. More than 37 million Americans have disabilities and the majority of disabled children spend a good part of their day in regular classes. As educators, we find many representatives of this diverse population in our classrooms. We have an obligation to teach all of these children and to do so effectively. In order to be effective, we must understand, accept, and address our students' differences. In educational terms, acceptance of diversity has come to be known as multicultural education. More precisely, multicultural education is the term used "to describe educational policies and practices that recognize, accept, and affirm human differences and similarities related to gender, race, handicap, and class" (Sleeter and Grant, 1988, p. 137). The purpose of this article is to provide guidelines for teaching reading in a multicultural framE3work, to discuss why, when and how to use multicultural literature, and to offer criteria for choosing good multicultural literature. Barry, A. L. (1990). Teaching Reading in a Multicultural Framework. Reading Horizons, 31 (1). Retrieved from https://scholarworks.wmich.edu/reading_horizons/vol31/iss1/5

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In this grammar worksheet, students read forty sentences and rewrite the ones that are fragments into complete sentences and place a c next to the ones that are correct as is. 6 Views 9 Downloads - Activities & Projects - Graphics & Images - Handouts & References - Lab Resources - Learning Games - Lesson Plans - Primary Sources - Printables & Templates - Professional Documents - Study Guides - Graphic Organizers - Writing Prompts - Constructed Response Items - AP Test Preps - Lesson Planet Articles - Interactive Whiteboards - All Resource Types - Show All See similar resources: Comma Splices, Fragments, and Run-Ons Differentiate between comma splices, fragments, and run-ons with this handout. Each punctuation error is coupled with distinct definitions and examples. Though this handout does not require learner participation, it is a useful guide for... 7th - 12th English Language Arts Fragments, Comma Splices, and Fused Sentences This excellent resource has the audience focus on ways to create complete sentences. As the presentation progresses, they see many examples of sentences that are fragments, run-ons, and ones that are punctuated incorrectly. They then... 4th - 7th English Language Arts CCSS: Adaptable Independent Clauses, Dependent Clauses, & Fragments When is a clause a complete sentence, and when do you need to add a subordinate conjunction? Practice complex sentences and avoid fragments with a grammar video. With fun pictures and interesting graphics, the video will get through to... 4 mins 4th - 8th English Language Arts CCSS: Adaptable New Review Fragments and Run-ons English teachers around the world cringe when they come across fragments and run-ons in papers. A handout on these poor imitations of sentences helps bring relief by reviewing the basics of sentence construction and by offering... 9th - Higher Ed English Language Arts CCSS: Adaptable Eliminate Fragments and Run-ons Fix fragments and run-ons. Kids practice editing a piece of their own writing, read, and take notes of common examples. They practice connecting independent clauses and then use the information to edit previously written pieces. Note:... 4th - 8th English Language Arts

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Rarely does a noun hang around on its own. Besides the comfortable companionship of adjectives, nouns tend to keep certain words close to them. These words, which you and your students know as articles, determiners, and quantifiers, help the reader or listener know which of a multitude of nouns the speaker is referring to. The question is, how does a person use them? And how does someone teach their ESL students how to use them correctly? While many ESL students will have little to no trouble with these often tiny words, some students have native languages which do not use articles or use a completely different system for choosing articles. What follows is a breakdown of these noun companions and how to teach them to your students. They may find that these little English words are a whole lot of trouble. What Are Determiners? Determiners are a class of words in the English language that point out which of a particular noun a speaker is referring to. They are not a part of speech but are actually a linguistic category of words. Determiners can be used to refer to a specific noun or a general noun. In some ways, they are like adjectives, giving additional information about the noun with which they are paired, but there are a limited number of determiners in the English language. And while not every noun has a determiner, a noun never has more than one determiner. There are several classes of English words which fall under the category of determiner: articles, numbers, indefinite pronouns, demonstrative pronouns, and possessive pronouns. Read on to learn more about each of these parts of speech. English has three articles – the, a, and an. These simple little words tell the listener what particular noun a speaker is referring to. The refers to a specific noun. It refers to the only one of that particular noun in existence (the Sears Tower), or it may refer to a specific noun that was mentioned earlier in the sentence or conversation. (I bought a book. The book is on the table.) A, on the other hand, is a general article. When used with a noun, it refers to any of that particular noun in existence. (He ate a pear.) It is not referring to one specific noun nor is its unique identity important. An works the same way as a with one difference. English speakers use a before nouns which begin with consonant sound, an before words which begin with vowel sounds (a book, a ride, an apple, an egg). Note that it is not spelling which determines whether to use a or an but the initial sound (a university, an hour). Some is sometimes referred to as an article though technically it is an indefinite pronoun. Some teachers choose to tell their students that some is the plural form of a or an since the latter are only used with singular nouns. The can be used with either singular or plural nouns. Teach These Small Words with Expertise Numbers are one of the first things an ESL student studies. In fact, learning to count in some foreign language is something almost anyone can do. But counting and using numbers as determiners are not exactly the same thing. When a number is used as a determiner, it comes before the noun and specifies the specific number of that noun to which the speaker is referring. Sam had two books, six pencils, and four assignments. Indefinite pronouns are those which do not refer to a specific noun. In that way, they are similar to the word a, but they give more information than it does. Indefinite pronouns include anyone, anywhere, somewhere, someone, more, several, few, many, both, all, and any. Anyone and someone refer to a nonspecific person. Anywhere and somewhere refer to a nonspecific person. More is used to mean in addition (I want more cake). Few, several, and many refer to a general amount of a given noun (He as read several books). Both and all refer to all of an item, whether the number is unspecified or the number is two (as in the case with both). In most cases, an indefinite pronoun can be replaced with a, an, or some in a sentence without affecting the grammar of the sentence, but it will slightly affect the meaning of the sentence. - She has some books. (an unspecified number) - She has many books. (an unspecified large number) - She has few books. (an unspecified small number) English has four demonstrative pronouns: this, that, these, and those. They are used to refer to specific nouns that are either singular or plural and are relatively near the speaker. This refers to a singular noun near the speaker. These refers to a plural noun near the speaker. That refers to a singular noun that is farther away from the speaker. Those refers to a plural noun that is farther away from the speaker. There is no hard and fast rule whether to use this or that, these or those. The specific distance does not determine the word choice. It is the general impression of the speaker which determines which word is the best choice in given circumstances. A possessive pronoun is used to show possession of a noun. English has a finite set of possessive pronouns: my, your, his, her, its, our, and their. These pronouns agree in number with the noun showing ownership. - My coat is on the back of his chair. Quantifiers are worth a mention here though they are NOT determiners. Quantifiers are used with a noncount noun to make that item countable. They do not fill the role of a determiner. They are actually nouns and are preceded by their own determiners. - He carried a bucket of water. In the previous sentence, bucket is the noun and a is the determiner (article). Water is also a noun, but in this sentence it is the object of the preposition. It does not have a determiner though it is possible for a noncount noun in a prepositional phrase to also have a determiner as in the following sentence. - Have a cup of this coffee. It is delicious. Though there are many types of determiners in English, each noun we find will only use one of them. Often, it is best to introduce one type of determiner to your students at a time. As you do, be sure to point out to your students that they are members of the linguistic category or class of determiners and are not a part of speech though several parts of speech belong to the class of determiners. Which type of determiner is the biggest struggle for your students? P.S. If you enjoyed this article, please help spread it by clicking one of those sharing buttons below. And if you are interested in more, you should follow our Facebook page where we share more about creative, non-boring ways to teach English.

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- Displaying Basic Information - Manipulating Variable Values with Operators - Understanding Punctuators - Moving Values with the Assignment Operator - Working with Mathematical/Arithmetic Operators - Making Comparisons with Relational Operators - Understanding Logical Bitwise Operators - Understanding the Type Operators - Using the sizeof Operator - Shortcutting with the Conditional Operator - Understanding Operator Precedence - Converting Data Types - Understanding Operator Promotion - Bonus Material: For Those Brave Enough How important is it to understand operators and operator precedence? You will use the operators in almost every application you create. Operator precedence is critical to understand. As you saw in today's lesson, if you don't understand operator precedence, you might end up with results that are different from what you expect. Today's lesson covered the binary number system briefly. Is it important to understand this number system? Also, what other number systems are important? Although it is not critical to understand binary, it is important. With computers today, information is stored in a binary format. Whether it is a positive versus negative charge, a bump versus an impression, or some other representation, all data is ultimately stored in binary. Knowing how the binary system works will make it easier for you to understand these actual storage values. In addition to binary, many computer programmers work with octal and hexadecimal. Octal is a base-8 number system, and hexadecimal is a base-16 number system. Appendix C, "Understanding Number Systems," covers these systems in more detail.

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In elementary school, we all learned the vowels of the English language: a, e, i, o, u and sometimes y. But what makes a vowel a vowel? Vowels and consonants are essentially two different categories of sounds that linguists use to better understand how language sounds work. The study of the sounds that human beings can produce is called phonetics. It’s a sub-speciality of linguistics. According to phoneticians, a vowel is a speech sound that is made without constriction of the vocal tract. What does that mean? It means that when you say a vowel, the sound is not stopped by your tongue, teeth, or cheeks. Try it! When you pronounce all of the vowels, your mouth stays open, but for every consonant, your tongue hits your teeth or the top of your mouth. Every language has vowels, though some have more vowel sounds than others. Across many languages, all words have to have vowel sounds, but not all words have to have consonants. This is because the sound and volume of spoken language comes from the vowels. The consonants break up the sound that the vowels generate. That’s why it’s impossible to say a string of consonants in a row. By nature, consonants stop the air flowing through the vocal tract, which is why you can say a vowel as long as you have breath, but you can’t draw out a sound like “l” unless you break it up with more vowels, as in “lalala.” This is also why vowels sit in the middle of syllables. They give language form and rhythm. Strings of consonants sound like parts of words in English. Think of the phrases, “hmm” or “hmph.” They are not complete words, even though they do have some meaning. Without any vowels in languages, we would be left with meaningless consonant strings. Although some languages, like Polish, can have as many as five consonants in a row, in English, we’re typically restricted to three, like str in strict. Vowels and consonants are oversimplified categories, of course—sounds are in reality more complicated than that. Take sounds like “s” or “z,” which don’t need to be broken up by vowels to continue. Are they vowels or consonants? You can say “z” forever. It’s the onomatopoetic sound of bees buzzing, to give just one example. These sounds are a subcategory of consonants called fricatives, made by pushing air through a very small space in your mouth. And what about y? Y is an example of a semivowel. Learn more about the history of the 25th letter of the alphabet here. English is a complicated language. What other facets of the English language stump you?

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About this worksheet: This worksheet is meant to allow the teacher to grade for correct answers quickly and accurately without grading every single problem by hand. You should tell the students that the dots will not form a picture like they are used to. You can tell them that if they do it correctly then a regular hexagon can be found somewhere on the page (it is not necessary to tell them though), but it may not be made with the dots on the paper. The hexagon is for you to help identify whether or not students did the bulk of the worksheet correctly. Note that the regular hexagon is formed by making straight line segments from point to point, so the students do need to use a straightedge when connecting the dots. Interpret the structure of expressions. Interpret expressions that represent a quantity in terms of its context.* Interpret parts of an expression, such as terms, factors, and coefficients. Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2). Write expressions in equivalent forms to solve problems. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* Factor a quadratic expression to reveal the zeros of the function it defines.

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New work from an international team of researchers including Carnegie's Lara Wagner improves our understanding of the geological activity that is thought to have formed the Rocky Mountains. It is published by Nature. Subduction is a geological process that occurs at the boundary between two of the many plates that make up the Earth's crust. An oceanic crustal plate sinks and slides under another plate—either oceanic or continental—and is plunged deep into Earth's mantle. Usually the lower plate slides down into the mantle at a fairly steep angle, sinking rapidly into the warmer, less-dense mantle material. However, in a process called "flat-slab" subduction, the lower plate moves nearly horizontally underneath the upper plate, sometimes for great distances. Flat-slab subduction is used to explain volcanism and mountain formation that occurs far from plate boundaries, because the lower, "flat" slab moves inland beneath the surface of a landmass and thereby transmits the friction of the plates sliding against one another far inland. The formation of the Rocky Mountains between 55 and 80 million years ago, according to sedimentary and volcanic records that have been studied in detail since the 1970s, often is attributed to flat-slab subduction as the plate beneath the Pacific Ocean at that time slid beneath the North American continent. Today, the largest flat slab is found beneath Peru, where the oceanic Nazca Plate is being subducted under the continental South American Plate. An undersea mountain belt, called the Nazca Ridge, sits on the Nazca Plate, and has been subducted along with the rest of the plate for the past 11 million years, according to previous studies Although scientists knew that a flat slab existed in this region, much about how and when it was formed has remained a mystery. Using an array of seismometers placed over the region of flat-slab subduction, the team was able to image the structure of the subducted plate in unprecedented detail. This allowed the team to study the evolution of the Peruvian flat slab over time and to better understand the forces that created and sustain it. What they found is that the angle of subduction is shallowest where the Nazca Ridge is being subducted beneath Peru. The portion of the plate containing this ridge sinks about 90 kilometers (56 miles) down and then flattens out. Away from the ridge, older portions of the flat slab that are no longer supported by the thick crust of the Nazca Ridge are found to be sagging, and younger, more recently subducted oceanic crust has torn free of the old, flat slab and is subducting at a normal dip angle. "This was surprising as we expected to image large, older flat slab to the north. Instead, we found that the flat slab north of the subducting Nazca Ridge tears and reinitiates normal, steep subduction," said lead author Sanja Knezevic Antonijevic, a student at the College of Arts and Sciences at the University of North Carolina at Chapel Hill. Suction and trench retreat previously were theorized to be sufficient to create a flat slab. Suction is created between the upper plate and the downgoing slab, because the surrounding mantle is too viscous to creep into the narrow space between the two plates. Trench retreat occurs when the subducting oceanic plate moves dominantly downward, not laterally forward, resulting in an oceanward migration of the continent and trench. However the team's model shows that the subduction of the ridge is necessary for the flat slab's formation, presumably because the buoyancy of the volcanically thickened Nazca Ridge keeps this portion of the plate from plunging steeply into the mantle. What's more, removing the ridge from the model causes the flat slab to become unstable. "Our model provides insights into the way that the Peruvian flat slab formed and evolved over time that can be applied to the studies of other flat-slab subduction events, such as the one that formed the Rocky Mountains," Wagner said. Provided by: Carnegie Institution for Science

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In this series on estimation and rounding, you will learn about methods to teach your children about how to estimate and round through hands-on activities. These are important skills to learn, that as adults, we use in our everyday lives. It is also a recurring topic that is covered in almost every grade level of math from first grade through high school. Learning to Estimate to the Nearest 10 This first topic in this series is about learning to estimate to the nearest 10. As an introduction for you and your child,, you can watch this video on rounding to the nearest ten. This can provide practice based upon numbers on a number line, with rounding up from 5 and down from 4. The video provides tips that will set the stage for more learning activities. A fun activity for this topic is to provide you child with a set of toys, candies, cereal, or other objects that they can count. Before they count them, you can have them estimate to the nearest 10 how many there are in all. Legos provide a great toy to use for this activity because you have many of them and then can add or subtract to to have your child re-estimate for quick practice. You can even have them estimate based on color or shape. Candies or cereals also provide a good object for tangible practice. You can add more or have them snack to take away. In addition to learning estimation, they can also practice counting, skip counting (by 2’s, 5’s, or 10’s), addition, and subtraction skills. What activities do you do with your children to practice estimation at home? Check back for more about estimation and rounding later this week.

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Comprehension Instruction: What Works Reading is often thought of as a hierarchy of skills, from processing of individual letters and their associated sounds to word recognition to text-processing competencies. Skilled comprehension requires fluid articulation of all these processes, beginning with the sounding out and recognition of individual words to the understanding of sentences in paragraphs as part of much longer texts. There is instruction at all of these levels that can be carried out so as to increase student understanding of what is read. - Teach decoding skills - Teach vocabulary - Word knowledge Encourage students to build world knowledge through reading and to relate what they know to what they read (e.g., by asking "Why?" questions about factual knowledge in text). - Active comprehension strategies Teach students to use a repertoire of active comprehension strategies, including prediction, analyzing stories with respect to story grammar elements, question asking, image construction, and summarizing. Encourage students to monitor their comprehension, noting explicitly whether decoded words make sense and whether the text itself makes sense. When problems are detected, students should know that they need to reprocess (e.g., by attempting to sound out problematic words again or rereading). Such instruction must be long term, for there is much to teach and much for young readers to practice. Even so, there is little doubt that instruction that develops these interrelated skills should improve comprehension. Perhaps it is a truism, but students cannot understand texts if they cannot read the words. Before they can read the words, they have to be aware of the letters and the sounds represented by letters so that sounding out and blending of sounds can occur to pronounce words (see, e.g., Nicholson, 1991). Once pronounced, the good reader notices whether the word as recognized makes sense in the sentence and the text context being read and, if it does not, takes another look at the word to check if it might have been misread (e.g., Gough, 1983, 1984). Of course, reading educators have paid enormous attention to the development of children's word-recognition skills because they recognize that such skills are critical to the development of skilled comprehenders. As part of such work, LaBerge and Samuels (1974) made a fundamental discovery. Being able to sound out a word does not guarantee that the word will be understood as the child reads. When children are first learning to sound out words, it requires real mental effort. The more effort required, the less consciousness left over for other cognitive operations, including comprehension of the words being sounded out. Thus, LaBerge and Samuels' analyses made clear that it was critical for children to develop fluency in word recognition. Fluent (i.e., automatic) word recognition consumes little cognitive capacity, freeing up the child's cognitive capacity for understanding what is read. Anyone who has ever taught elementary children and witnessed round-robin reading can recall students who could sound out a story with great effort but at the end had no idea of what had been read. Tan and Nicholson (1997) carried out a study that emphasized the importance of word-recognition instruction to the point of fluency. In their study, struggling primary-level readers were taught 10 new words, with instruction either emphasizing word recognition to the point of fluency (they practiced reading the individual words until they could recognize them automatically) or understanding of the words (instruction involving mostly student-teacher discussions about word meanings). Following the instruction, the students read a passage containing the words and answered comprehension questions about it. The students who had learned to recognize the words to the point of automaticity answered more comprehension questions than did students who experienced instruction emphasizing individual word meanings. Consistent with other analyses (e.g., Breznitz, 1997a, 1997b), Tan and Nicholson's outcome made obvious that development of fluent word-recognition skills can make an important difference in students' understanding of what they read. Thus, a first recommendation to educators who want to improve students' comprehension skills is to teach them to decode well. Explicit instruction in sounding out words, which has been so well validated as helping many children to recognize words more certainly (e.g., Snow, Burns, & Griffin, 1998, online document), is a start in developing good comprehenders but it is just a start. Word-recognition skills must be developed to the point of fluency if comprehension benefits are to be maximized. It is well established that good comprehenders tend to have good vocabularies (Anderson & Freebody, 1991; Nagy, Anderson, & Herman, 1987). This correlation, however, does not mean that teaching vocabulary will increase readers' comprehension, for that is a causal conclusion. As it turns out, however, when reading educators conducted experiments in which vocabulary was either taught to students or not, comprehension improved as a function of vocabulary instruction. Perhaps the most widely cited experiment of this type was carried out by Isabel Beck and her associates, who taught Grade 4 children a corpus of 104 words over a 5-month period (Beck, Perfetti, & McKeown, 1982). The children who received instruction outperformed noninstructed children on subsequent comprehension tests. When all of the work of Beck's group and others is considered (see, e.g., Beck & McKeown, 1991; Durso & Coggins, 1991), a good case can be made that when students are taught vocabulary in a thorough fashion, their comprehension of what they read improves. One counterargument to this advice to teach vocabulary is that children learn vocabulary incidentally that is, they learn the meanings of many words by experiencing those words in the actual world and in text worlds, without explicit instruction (Stanovich, 1986; Sternberg, 1987). Even so, such incidental learning is filled with potential pitfalls, for the meanings learned range from richly contextualized and more than adequate to incomplete to wrong (Miller & Gildea, 1987). Just the other morning, I sat in a reading class as a teacher asked students to guess the meanings of new words encountered in a story, based on text and picture clues. Many of the definitions offered by the children were way off. Anyone who has ever taught young children knows that they benefit from explicit teaching of vocabulary. That children do develop knowledge of vocabulary through incidental contact with new words they read is one of the many reasons to encourage students to read extensively. Whenever researchers have looked, they have found vocabulary increases as a function of children's reading of text rich in new words (e.g., Dickinson & Smith, 1994; Elley, 1989; Morrow, Pressley, Smith, & Smith, 1997; Pelligrini, Galda, Perlmutter, & Jones, 1994; Robbins & Ehri, 1994; Rosenhouse, Feitelson, Kita, & Goldstein, 1997). Reading comprehension can be affected by world knowledge, with many demonstrations that readers who possess rich prior knowledge about the topic of a reading often understand the reading better than classmates with low prior knowledge (Anderson & Pearson, 1984). That said, readers do not always relate their world knowledge to the content of a text, even when they possess knowledge relevant to the information it presents. Often, they do not make inferences based on prior knowledge unless the inferences are absolutely demanded to make sense of the text (McKoon & Ratcliff, 1992). The received wisdom in recent decades, largely based on the work of Richard C. Anderson, P. David Pearson, and their colleagues at the Center for the Study of Reading at the University of Illinois in the 1970s, 1980s, and into the early 1990s, was that reading comprehension can be enhanced by developing reader's prior knowledge. One way to accomplish this is to encourage extensive reading of high-quality, information-rich texts by young readers (e.g., Stanovich & Cunningham, 1993). Typically, however, when readers process text containing new factual information, they do not automatically relate that information to their prior knowledge, even if they have a wealth of knowledge that could be related. In many cases, more is needed for prior knowledge to be beneficial in reading comprehension. A large number of experiments conducted in the late 1980s and early 1990s demonstrated the power of "Why?" questions, or "elaborative interrogation," to encourage readers to orient to their prior knowledge as they read (Pressley, Wood, Woloshyn, Martin, King, & Menke, 1992). In these studies, readers were encouraged to ask themselves why the facts being presented in text made sense. This encouragement consistently produced a huge effect on memory of the texts, with the most compelling explanation emerging from analytical experiments being that the interrogation oriented readers to prior knowledge that could explain the facts being encountered (see especially Martin & Pressley, 1991). The lesson that emerged from these studies is that readers should be encouraged to relate what they know to information-rich texts they are reading, with a potent mechanism for doing this being elaborative interrogation. Active comprehension strategies Good readers are extremely active as they read, as is apparent whenever excellent adult readers are asked to think aloud as they go through text (Pressley & Afflerbach, 1995). Good readers are aware of why they are reading a text, gain an overview of the text before reading, make predictions about the upcoming text, read selectively based on their overview, associate ideas in text to what they already know, note whether their predictions and expectations about text content are being met, revise their prior knowledge when compelling new ideas conflicting with prior knowledge are encountered, figure out the meanings of unfamiliar vocabulary based on context clues, underline and reread and make notes and paraphrase to remember important points, interpret the text, evaluate its quality, review important points as they conclude reading, and think about how ideas encountered in the text might be used in the future. Young and less skilled readers, in contrast, exhibit a lack of such activity (e.g., Cordón & Day, 1996). Reading researchers have developed approaches to stimulating active reading by teaching readers to use comprehension strategies. Of the many possible strategies, the following often produce improved memory and comprehension of text in children: generating questions about ideas in text while reading; constructing mental images representing ideas in text; summarizing; and analyzing stories read into story grammar components of setting, characters, problems encountered by characters, attempts at solution, successful solution, and ending (Pearson & Dole, 1987; Pearson & Fielding, 1991; Pressley, Johnson, Symons, McGoldrick, & Kurita, 1989). Of course, excellent readers do not use such strategies one at a time, nor do they use them simply when under strong instructional control which was the situation in virtually all investigations of individual strategies. Hence, researchers moved on to teaching students to use the individual strategies together, articulating them in a self-regulated fashion (i.e., using them on their own, rather than only on cue from the teacher). In general, such packages proved teachable, beginning with reciprocal teaching, the first such intervention (Palincsar & Brown, 1984), and continuing through more flexible approaches that began with extensive teacher explanation and modeling of strategies, followed by teacher-scaffolded use of the strategies, and culminating in student self-regulated use of the strategies during regular reading (e.g., Anderson, 1992; Brown, Pressley, Van Meter, & Schuder, 1996; Duffy et al., 1987). The more recent, more flexible form of this instruction came to be known as transactional strategies instruction (Pressley et al., 1992), with the body of research on this approach recently cited by the National Reading Panel (2000) as exemplary work in comprehension instruction. When such instruction has been successful, it has always been long term, occurring over a semester or school year at minimum, with consistent and striking benefits. The case is very strong that teaching elementary, middle school, and high school students to use a repertoire of comprehension strategies increases their comprehension of text. Teachers should model and explain comprehension strategies, have their students practice using such strategies with teacher support, and let students know they are expected to continue using the strategies when reading on their own. Such teaching should occur across every school day, for as long as required to get all readers using the strategies independently which means including it in reading instruction for years. Good readers know when they need to exert more effort to make sense of a text. For example, they know when to expend more decoding effort they are aware when they have sounded out a word but that word does not really make sense in the context (Isakson & Miller, 1976). When good readers have that feeling, they try rereading the word in question. It makes sense to teach young readers to monitor their reading of words in this way (Baker & Brown, 1984). Contemporary approaches to word-recognition instruction also include a monitoring approach, with readers taught to pay attention to whether the decoding makes sense and to try decoding again when the word as decoded is not in synchrony with other ideas in the text and pictures (e.g., Iversen & Tunmer, 1993). Good readers are also aware of the occasions when they are confused, when text does not make sense (Baker & Brown, 1984). A key component in transactional strategies instruction is monitoring. Even the first such package, reciprocal teaching (Palincsar & Brown, 1984), included the clarification strategy: When readers did not understand a text, they were taught to seek clarification, often through rereading. To improve children's reading and comprehension, it makes very good sense to teach them to monitor as they read, to ask themselves consistently, "Is what I am reading making sense?" Children also need to be taught that they can do something about it when text seems not to make sense: At a minimum, they can try sounding out a puzzling word again or rereading the part of a text that seems confusing. This technique is recommended by research Reading comprehension instruction has been recommended as a practice with solid research evidence of effectiveness for individuals with learning disabilities by the Council for Exceptional Children — the Division for Learning Disabilities (DLD) and the Division for Research (DR). To learn more, please read A Focus on Reading Comprehension Strategy Instruction. Click the "References" link above to hide these references. Anderson, R.C., & Freebody, P. (1981). Vocabulary knowledge. In J.T. Guthrie (Ed.), Comprehension and teaching: Research reviews (pp. 77-117). Newark DE: International Reading Association. Anderson, R.C., & Pearson, P.D. (1984). A schema-theoretic view of basic processes in reading. In P.D. Pearson, R. Barr, M.L. Kamil, & P. Mosenthal (Eds.), Handbook of reading research. White Plains, NY: Longman. Anderson, V. (1992). A teacher development project in transactional strategy instruction for teachers of severely reading-disabled adolescents. Teaching & Teacher Education, 8, 391-403. Baker, L., & Brown, A.L. (1984). Metacognitive skills and reading. In P.D. Pearson, R. Barr, M.L. Kamil, & P. Mosenthal (Eds.), Handbook of reading research (pp. 353-394). White Plains, NY: Longman. Beck, I.L., & McKeown, M. (1991). Conditions of vocabulary acquisition. In R. Barr, M.L. Kamil, P. Mosenthal, & P.D. Pearson (Eds.), Handbook of reading research: Volume II (pp. 789-814). White Plains, NY: Longman. Beck, I.L., Perfetti, C.A., & McKeown, M.G. (1982). Effects of long term vocabulary instruction on lexical access and reading comprehension. Journal of Educational Psychology, 74, 506-521. Block, C.C., & Pressley, M. (Eds.). (in press). Comprehension instruction. New York: Guilford. Breznitz, Z. (1997a). Effects of accelerated reading rate on memory for text among dyslexic readers. Journal of Educational Psychology, 89, 289-297. Breznitz, Z. (1997b). Enhancing the reading of dyslexic children by reading acceleration and auditory masking. Journal of Educational Psychology, 89, 103-113. Brown, R., Pressley, M., Van Meter, P., & Schuder, T. (1996). A quasi-experimental validation of transactional strategies instruction with low-achieving second grade readers. Journal of Educational Psychology, 88, 18-37. Cordon, L.A., & Day, J.D. (1996). Strategy use on standardized reading comprehension tests. Journal of Educational Psychology, 88, 288-295. Dickinson, D.K., & Smith, M.W. (1994). Long-term effects of preschool teachers' book readings on low-income children's vocabulary and story comprehension. Reading Research Quarterly, 29, 104-122. Duffy, G.G., Roehler, L.R., Sivan, E., Rackliffe, G., Book, C., Meloth, M., Vavrus, L.G., Wesselman, R., Putnam, J., & Bassiri, D. (1987). Effects of explaining the reasoning associated with using reading strategies. Reading Research Quarterly, 22, 347-368. Durkin, D. (1978-79). What classroom observations reveal about reading comprehension instruction. Reading Research Quarterly, 14, 481-533. Durso, F.T., & Coggins, K.A. (1991). Organized instruction for the improvement of word knowledge skills. Journal of Educational Psychology, 83, 109-112. Eco, U. (1990). The limits of interpretation. Bloomington IN: Indiana University Press. Elley, W.B. (1989). Vocabulary acquisition from listening to stories. Reading Research Quarterly, 24, 174-187. Flower, L., Stein, V., Ackerman, J., Kantz, M.J., McCormick, K., & Peck, W.C. (1990). Reading to write: Exploring a cognitive and social process. New York: Oxford University Press. Gough, P.D. (1983). Context, form, and interaction. In K. Rayner (Ed.), Eye movements in reading (pp. 203-211). New York: Academic. Gough, P.B. (1984). Word recognition. In P.D. Pearson, R. Barr, M.L. Kamil, & P. Mosenthal (Eds.), Handbook of reading research (pp. 225-254). White Plains, NY: Longman. Gough, P.B., Hoover, W.A., & Peterson, C.L. (1996). Some observations on a simple view of reading. In C. Cornoldi & J. Oakhill (Eds.), Reading comprehension difficulties (pp. 1-13). Mahwah, NJ: Erlbaum. Guthrie, J.T. (1988). Locating information in documents: Examination of a cognitive model. Reading Research Quarterly, 23, 178-199. Isakson, R.L., & Miller, J.W. (1976). Sensitivity to syntactic and semantic cues in good and poor comprehenders. Journal of Educational Psychology, 68, 787-792. Iversen, S., & Tunmer, W.E. (1993). Phonological processing skills and the Reading Recovery program. Journal of Educational Psychology, 85, 112-120. Kamil, M.L., Mosenthal, P.B., Pearson, P.D., & Barr, R. (Eds.). (2000). Handbook of reading research: Volume III. Mahwah, NJ: Erlbaum. Keene, E.O., & Zimmermann, S. (1997). Mosaic of thought: Teaching comprehension in a reader's workshop. Portsmouth NH: Heinemann. LaBerge, D., & Samuels, S.J. (1974). Toward a theory of automatic information processing in reading. Cognitive Psychology, 6, 293-323. Martin, V.L., & Pressley, M. (1991). Elaborative-interrogation effects depend on the nature of the question. Journal of Educational Psychology, 83, 113-119. McKoon, G., & Ratcliff, R. (1992). Inference during reading. Psychological Review, 99, 440-466. Miller, G.A., & Gildea, P. (1987). How children learn words. Scientific American, 257(3), 94-99. Morrow, L.M., Pressley, M., Smith, J.K., & Smith, M. (1997). The effect of a literature-based program integrated into literacy and science instruction with children from diverse backgrounds. Reading Research Quarterly, 32(1), 55-76. Nagy, W., Anderson, R., & Herman, P. (1987). Learning word meanings from context during normal reading. American Educational Research Journal, 24, 237-270. National Reading Panel. (2000, April). Report of the National Reading Panel: Teaching children to read. Washington, DC: National Institute of Child Health and Human Development, National Institutes of Health, U.S. Department of Health and Human Services. Available: www.nichd.nih.gov/publications/pubskey.cfm?from=nrp Nicholson, T. (1991). Do children read words better in context or in lists? A classic study revisited. Journal of Educational Psychology, 83, 444-450. Palincsar, A.S., & Brown, A.L. (1984). Reciprocal teaching of comprehension-fostering and monitoring activities. Cognition and Instruction, 1, 117-175. Pearson, P.D., & Dole, J.A. (1987). Explicit comprehension instruction: A review of research and a new conceptualization of instruction. Elementary School Journal, 88, 151-165. Pearson, P.D., & Fielding, L. (1991). Comprehension instruction. In R. Barr, M.L. Kamil, P.B. Mosenthal, & P.D. Pearson (Eds.), Handbook of reading research: Volume II (pp. 815-860). White Plains, NY: Longman. Pellegrini, A.D., Galda, L., Perlmutter, J., & Jones, I. (1994). Joint reading between mothers and their Head Start children: Vocabulary development in two text formats (Reading Research Rep. No. 13). Athens, GA, & College Park, MD: National Reading Research Center. Pressley, M. (2000). What should comprehension instruction be the instruction of? In M.L. Kamil, P.B. Mosenthal, P.D. Pearson, & R. Barr (Eds.), Handbook of reading research: Volume III (pp. 545-561). Mahwah NJ: Erlbaum. Pressley, M., & Afflerbach, P. (1995). Verbal protocols of reading: The nature of constructively responsive reading. Hillsdale NJ: Erlbaum. Pressley, M., & El-Dinary, P.B. (1997). What we know about translating comprehension strategies instruction research into practice. Journal of Learning Disabilities, 30, 486-488. Pressley, M., El-Dinary, P.B., Gaskins, I., Schuder, T., Bergman, J., Almasi, L., & Brown, R. (1992). Beyond direct explanation: Transactional instruction of reading comprehension strategies. Elementary School Journal, 92, 511-554. Pressley, M., Johnson, C.J., Symons, S., McGoldrick, J.A., & Kurita, J.A. (1989). Strategies that improve children's memory and comprehension of text. Elementary School Journal, 90, 3-32. Pressley, M., Wharton-McDonald, R., Hampson, J.M., & Echevarria, M. (1998). The nature of literacy instruction in ten grade-4/5 classrooms in upstate New York. Scientific Studies of Reading, 2, 159-191. Pressley, M., Wood, E., Woloshyn, V.E., Martin, V., King, A., & Menke, D. (1992). Encouraging mindful use of prior knowledge: Attempting to construct explanatory answers facilitates learning. Educational Psychologist, 27, 91-110. Robbins, C., & Ehri, L.C. (1994). Reading storybooks to kindergartners helps them learn new vocabulary words. Journal of Educational Psychology, 86, 54-64. Rosenblatt, L.M. (1938). Literature as exploration. New York: Progressive Education Association. Rosenblatt, L.M. (1978). The reader, the text, the poem: The transactional theory of the literary work. Carbondale, IL: Southern Illinois University Press. Rosenhouse, J., Feitelson, D., Kita, B., & Goldstein, Z. (1997). Interactive reading aloud to Israeli first graders: Its contribution to literacy development. Reading Research Quarterly, 32, 168-183. Snow, C.E., Burns, M.S., & Griffin, P. (Eds.). (1998). Preventing reading difficulties in young children. Washington DC: National Academy Press. Available: books.nap.edu/catalog/6023.html Stanovich, K. (1986). Matthew effects in reading: Some consequences of individual differences in the acquisition of literacy. Reading Research Quarterly, 21, 360-407. Stanovich, K.E., & Cunningham, A.E. (1993). Where does knowledge come from? Specific associations between print exposure and information acquisition. Journal of Educational Psychology, 85, 211-229. Sternberg, R.J. (1987). Most vocabulary is learned from context. In M.G. McKeown & M.E. Curtis (Eds.), The nature of vocabulary acquisition. Hillsdale, NJ: Erlbaum. Tan, A., & Nicholson, T. (1997). Flashcards revisited: Training poor readers to read words faster improves their comprehension of text. Journal of Educational Psychology, 89, 276-288. Williams, J.P. (1993). Comprehension of students with and without learning disabilities: Identification of narrative themes and idiosyncratic text representations. Journal of Educational Psychology, 85, 631-641.

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What is Equality and Diversity? Equality and diversity, or multiculturalism, is the idea of promoting and accepting the differences between people. More specifically, equality is about ensuring individuals are treated fairly and equally, no matter their race, gender, age, disability, religion or sexual orientation. Diversity is about recognising and respecting these differences to create an all-inclusive atmosphere. Promoting equality and diversity in education is essential for both teachers and students. The aim is to create a classroom environment where all students can thrive together and understand that individual characteristics make people unique and not ‘different’ in a negative way. How can equality and multiculturalism be promoted at school? Promoting equality and diversity in the classroom need not be a challenge and is something that all children should be familiar with from an early age. This means: - Setting clear rules in regards to how people should be treated. - Challenging any negative attitudes. - Treating all staff and students fairly and equally. - Creating an all-inclusive culture for staff and students. - Avoiding stereotypes in examples and resources. - Using resources with multicultural themes. - Actively promoting multiculturalism in lessons. - Planning lessons that reflect the diversity of the classroom. - Ensuring all students have equal access to opportunities and participation. - Making sure that learning materials do not discriminate against anyone and are adapted where necessary, e.g. large print or audio tape format. - Using a variety of teaching methods. - Using a variety of assessment methods. - Ensuring policies and procedures don’t discriminate against anyone. The Equality Act 2010 The Equality Act was introduced to offer legal protection to those people with one or more ‘protected characteristics’. The protected characteristics are: - Gender reassignment. - Marriage and civil partnership. - Pregnancy and maternity. - Religion or belief. - Sexual orientation. In regards to teaching this may mean: - Paying attention to the needs of students from diverse groups within your course design – including an equality analysis/impact assessment processes in your course development is a useful way of ensuring that you give due consideration to inclusivity and accessibility. - Making explicit to students the standards of conduct that you expect in the way that they interact and dealing promptly and appropriately with inappropriate behaviour. - Identifying opportunities within your teaching for students to work collaboratively in diverse groups. - Devising creative and respectful ways of using the diverse experiences of students to add value to the learning experience for everyone. Equality and Diversity Classroom Activities Is diversity included within your teaching methods? Do you make reference and use examples from a variety of cultures, religions and traditions? Do you challenge stereotypes? Here are a few classroom activities and ideas that you can use and adapt to help promote multiculturalism in your school: Host ‘African week’, ‘Islam week’ or ‘Disability week’ and teach your students all about the chosen topic. You could try different foods, listen to music, play games, learn facts and watch videos. Try and incorporate the theme into each area of the curriculum to reinforce the topic and maintain interest. Use diverse images in resources When you pick books, posters and activities for your students, make sure that they include people from different backgrounds or with disabilities to show that these differences are ‘normal’. Avoid resources where stereotypes are used. Make use of current news events Promote debate and discussion by raising current issues and seeing what your students understand about the situation. For example, find a story where someone was fired for being too old – what do your students think about this? How would they challenge it? Host weekly quizzes on a set theme and learn how much your students know about different cultures, religions, disabilities etc. You could even assign the task of writing the quiz to 2 students each week so that they are involved in doing the research. Set up a French café, Indian restaurant or American diner in your classroom and let your students sample foods typically eaten in the corresponding culture. What do they like or dislike about the foods? How is it different from what they normally have for dinner? Teach the students the reasons why certain foods are (or are not) eaten in certain countries. List things that come from abroad A quick activity you can do at the start of a lesson to introduce the theme of multiculturalism. Ask your students to create a list of everything in their life that comes from a country outside of the UK. Go through their responses as a class – are they surprised by the results? Male or female? Explore the idea of stereotypes – provide each student with a list of 10 professions and ask them to decide whether each is a ‘man’s job’ or a ‘woman’s job’. Go through their answers as a class and see what stereotypes people have. Is it fair that these stereotypes exist? How would they suggest these stereotypes are challenged? True or false? Present the class with some facts about people with disabilities, another culture or based on the protected characteristics and ask them to decide whether the facts are true or false. Are they surprised by the correct answers? Teach your students a few words in French, Spanish, Afrikaans, Chinese etc to raise their awareness of language barriers around the world. If you have students in your class who speak another language, ask them to help. What are the benefits of speaking more than one language? Hold debates and discussions Divide your class into 2 teams. Provide one team with a statement, e.g. ‘I’m a woman working in an office and have been told I can no longer work there because I recently became pregnant’. This team must defend this statement. Ask the other team to give advice and challenge the statement. How do both teams feel afterwards? Which team would they prefer to have been on and why? Hearing/sight/physical impairment games Play games to raise awareness of different physical disabilities. Can your students put on a jumper with just one hand? Can they guide a friend around the classroom with a blindfold on? Can they lip-read what the characters on TV are saying with the sound off? Use these activities to show the difficulties that people face and explain how these people learn to overcome them. This is a good activity for older students. Watch the YouTube video by the Guardian, but pause it after 10 seconds, 16 seconds and 24 seconds, taking time to ask the students what they think is happening in the video. Do their perceptions change as the video goes on? Get the students to justify their responses. You can find the video on YouTube. Find a few stories that challenge perceptions and stereotypes, such as the tortoise and the hare which proves that first impressions can be deceiving. These kind of stories will encourage your students to think about their beliefs and look at the world in a different way. Make your own jigsaws whereby facts need to match up with their country etc. You could also do this with different flags, national dresses or languages Host an event for Chinese new year, Diwali, Easter, Ramadan etc to raise awareness of different cultures and religions. Explain why each occasion is celebrated and ask your students what they enjoy most about them. Listen to music from around the world or create your own using percussion instruments. Introduce your class to instruments from other cultures that they may not have seen before and to different styles of music. If you have children with diverse cultural backgrounds in your class, perhaps they could do a show-and-tell? EducationEquality and DiversityTeachers and Parents Please share with your friends Louise uses her 4+ years of technical writing experience to write specialist articles on a range of health and safety, business skills and safeguarding people topics. Louise has a degree in English Language and enjoys pursuing a range of creative outlets, from writing and editing to baking, cooking and sewing. Evaluate How to Involve the Learner in the Assessment Process 2798 WordsJun 7th, 201312 Pages Roles and Responsibilities and Relationships in Lifelong Learning, Task 1-4 1.2 Analyse own responsibility for promoting equality and valuing diversity According to Urdany L, (1991). The definition of Equality; Sameness, Similarity, Likeness, resemblance, Equivalence, comparability, and comparison. The definition of Diversity; Difference, Unlikeness, Deviation, Distinctiveness, Variation, Contrast, discrepancy, Range, and Multiplicity. According to the Equality act, (2010) [When providing for learners they should all be treated equally despite] age, sex, sexual orientation,…show more content… Students will have identical rights and status. I will encourage students to challenge their own attitudes and beliefs so that they can appreciate and respect each other’s views situations and opinions. Learner assessments can be done to identify disability. I should be non-judgemental. I could use hand-outs which are representative of wider society. Before I organise trips, rewards, and incentives I will need to consider everybody’s individual needs and plan things that everybody can be included in as this will promote equality too. A good example of this is (Gravells A, 2008). A group of leaners wish to go out for dinner. One is vegetarian, another is dairy intolerant and a third does not eat fish. They all want to eat at the same restaurant and choose from the same menu and be treated equally, enabling them to choose a different option from the menu. The diverse requirements of the group are therefore being taken into account to differentiate for their needs. Other useful organisations that deal with the issues of equality and diversity are, The Disability Rights Commission, DRC. Equal Opportunities Commission, EOC. Commission for Racial Equality, CRE. 1.3 Evaluate own role and responsibility in lifelong learning. Evaluating my own roles and responsibilities will be an on-going factor. I will be eternally assessing my own judgements and capabilities; I will need to reflect and review

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TEFL / ESL – What is a Verb? What are Verbs? Verbs are words that are used to convey actions, states of being or relationships in the English language. They are one of the Parts of Speech and usually tell us what is going on in a sentence. This article outlines the different types of verbs, shows how to recognise them and explains their functions. As there are many ways to categorise verbs I will firstly outline Main Verbs, Auxiliary Verbs and Modal Verbs and then move unto other areas of distinction. Main Verbs, Auxiliary Verbs and Modal Verbs Main Verbs – These verbs can stand alone and the meaning is easily understood. Examples: I see her, He filmed the Cuban dawn, It comes with a warranty. Auxiliary Verbs – These are helping verbs and should not try to be understood on their own. The verb To Be, To Do and To Have allows us to change the tense of the verb, to make negatives and to ask questions. We don’t use them in the affirmative of the Present Simple or the Past Simple. Examples: They are going to Belgium, I didn’t see him yesterday, Have you eaten here before? Modal Verbs – These belong to the auxiliary verb category. They are used to express permission, obligation, possibility, logical deduction, requests, advice, suggestions, invitation and offers. They are not used on their own and precede the main verb without using To – I must visit Granpa. However, there are a number of differences; you do not modify the 3rd person with s/ies/es, e.g. They can hear you. There is no past tense except for the modal verb Can. Examples: Can, Should, May, Might, Could, Would, Will, Shall There are other modal verbs called ‘semi-modals’ which do not follow the rules outlined above. They are as follows: Need To, Have To, Ought To, To Be Able This list gives an even greater distinction of the types of verbs - - Regular verbs - Irregular verbs - Base form of a verb - Infinitive form of a verb - Present participle - Past participle - Action verbs - Stative verbs - Transitive verbs - Intransitive verbs - Linking verbs - Phrasal verbs Regular verbs – In the past simple these verbs are formed by adding d or ed. Examples: Arrived, Joined, Organised and Bathed. Irregular verbs – Have different past simple and past participle forms. Examples: Put, Ate, Had and Come. Base form verbs – Are the verbs you will find the dictionaries and do not have to preceding them. Examples: Take, Smell, Arrange and Pick. Infinitive – Form of the verb with to. Examples: To See, To Hear, To Run and To Fly. Present participle – The form of the verb with ing attached to the end. Examples: Sleeping, Crying, Feeling and Screaming. Past participle – Used to form tenses such as the present perfect or the passive and are used after verbs have and be. Regular verbs end in ed. Examples: Been, Gone, Walked and Played. Other Teaching Hubs Action – These verbs can be used with the continuous and the simple tenses and describe actions and events. Also known as Dynamic Verbs. Examples: Shout, Jump, Fall and Speak. Stative – Expresses a state or condition. They are not normally used with continuous tenses and they are associated with feelings, emotions, thinking, opinions and verbs that describe senses (Note that some verbs can be both action and stative verbs e.g. She’s having a shower, I have a red car). Examples: Prefer, Like, Understand and Know. Transitive – Need to be followed by an object – a noun, pronoun or a noun phrase. Examples: They named her Cindy, She broke a window, He gave her a flower, I’m watching this movie. Intransitive – Does not need to be followed by an object. Examples: She screamed like crazy, They sang, Yesterday we ate well, You slept. Linking – Needs to be followed by an adjective or a phrase with an adjective in it. These verbs do not express action. To differentiate between action verbs and linking verbs try substituting the linking verb with the verb To Be or an equals sign, e.g. I am hungry/I was hungry/I = hungry Examples: Be, Seem, Become. Verbs that are sometimes used as linking verbs depending on their function: Grow, Appear, Smell. Multiword – Combines a main verb and a particle. These can be phrasal verbs or prepositional verbs. Examples: She put off the wedding date, They drove away at high speed. © 2013 Muttface

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By examining the concept of "needs vs. wants," students learn that the things that make us happy are not necessarily things that cost money. Students will begin by discussing needs, wants, price, and value. Then they will watch the "Happiness" video, which will prompt further discussion and help students consider the relationship between consumer goods and happiness. This lesson can stand alone, or you can follow it with the companion lesson, Reduce, Reuse, Recycle. - Explain the difference between needs and wants, as well as price and value Grade Level: 1–2 - One class period (30 minutes) - Happiness Video Use these resources to create a simple assessment or video-based assignment with the Lesson Builder tool on PBS LearningMedia. - For each student: - 10 index cards or small (approximately 4" x 6") pieces of paper - pen or pencil - Computer or projector capable of playing video 1. (Estimated time, steps 1–5: 15 minutes) Introduce the lesson by explaining that things we want are sometimes different from things we need. You can give examples, such as we need food, but we want ice cream. 2. Ask students to generate responses to the question, What things give us a happy life? (Note: You may want to create categories to help structure responses: things for our body, things for our mind, things for our community.) Students should write or draw each item on a separate index card or small piece of paper. If you wish, you may also provide cards with images (food, house, clothing) for students to use to sort into categories. 3. Divide the class into small groups. Ask each group to combine their cards and sort them into two categories: needs and wants. Students may debate whether something is a need or a want. Help students explore what is common to all people, and why some responses may differ from others. (Ask, for example, What things do we ALL need? Can you give me an example of something that some people may need or want but others don't?) 4. Have students sort again, but this time into two categories: things that make them happy and things that cost money. Students may find that some things fit into both categories. Allow students to discuss their ideas. 5. Draw a Venn diagram on the board. Label one circle "Things That Make Us Happy." Label the other "Things That Cost Money." (Explain how the Venn diagram works, if needed.) Have students place their words in the proper place on the diagram, explaining as needed. 6. (Estimated time: steps 6–10: 15 minutes) Tell students to imagine that they will have 60 seconds to take anything they want from a toy store. Now tell students they are going to watch a short video about three kids who had such a shopping spree. 7. Watch the Happiness Video completely through one time. 8. Then, watch the Happiness Video again, pausing when the characters are shopping. Ask students, What is Clementine doing? 9. After finishing the video, ask students, Why do you think Clementine won? Some students may not believe Clementine was happier than the kids who got a lot of stuff. If this debate emerges, direct students with the following questions: - If you were in the video, what would be in your cart? (This directs students to identify WHAT exactly they want or need, moving them toward the realization that the boys weren't happy because they didn't know or value what they had.) - If you got all of those things, which item do you think would make you the happiest? Why? What would you tell Clementine about why you like that item so much? How is it similar to or different from what she loved about the pencils? 10. Help students move toward the general idea that many things that make us happy don't always cost money, things that are expensive don't always make us happy, and more is not always better. To conclude, ask students how they would change the story so that the boys were happier. What would have to be different? Check for Understanding - Ask students to identify something they already have that they cherish; this may include a sibling or a pet, again reinforcing the idea that happiness isn't dependent upon a purchase. - Ask students to bring in print advertisements for toys, and discuss these ads in class. Point out when an ad is unrealistic or promotes a stereotype. Use these questions for discussion prompts: - What is the ad telling you about this toy? What part do you think is true? What do you think is false? - Do you know of anyone who looks like that? who lives like that? Lesson developed in collaboration with Creative Change Educational Solutions.

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English Language Arts: Unit 1: Listen Like a Reader Length: 3 Weeks Unit 1 Focus: Letter names and sounds- m /m/; s /s/, short a /ă/ Language Arts Florida Standards: K.RL.1.1 With prompting and support, ask and answer questions about key details in a text. K.RL.2.5 Recognize common types of texts (e.g., storybooks, poems). K.RL.2.6 With prompting and support, identify the author and illustrator of a story and define the role of each in telling the story. K.RI.1.1 With prompting and support, ask and answer questions about key details in a text. K.RI.2.5 Identify the front cover, back cover, and title page of a book. (Level 1) K.RI.3.7 With prompting and support, describe the relationship between illustrations and the text in which they appear (e.g., what person, place, thing, or idea in the text an illustration depicts). K.L.3.5a Sort common objects into categories (e.g., shapes, foods) to gain a sense of the concepts the categories represent. K.L.1.1a Print many upper- and lowercase letters. K.L.1.1b Use frequently occurring nouns and verbs. K.W.1.3 Use a combination of drawing, dictating, and writing to narrate a single event or several loosely linked events, tell about the events in the order in which they occurred, and provide a reaction to what happened. K.RF.1.1a Follow words from left to right, top to bottom, and page by page. K.RF.1.1b Recognize that spoken words are represented in written language by specific sequences of letters. (Level 1) K.RF.1.1c Understand that words are separated by spaces in print. K.RF.1.1d Recognize and name all upper- and lowercase letters of the alphabet. K.RF.2.2a Recognize and produce rhyming words. K.RF.2.2b Count, pronounce, blend, and segment syllables in spoken words. K.RF.2.2c Blend and segment onsets and rimes of single-syllable spoken words. K.RF.2.2d Isolate and pronounce the initial medial vowel, and final sounds in three-phoneme words. K.RF.3.3a Demonstrate basic knowledge of letter-sound correspondences by producing the primary or most frequent sound for each consonant. K.RF.3.3b Associate the long and short sounds with the common spellings (graphemes) for the five major vowels. K.RF.3.3c Read common high-frequency words by sight. K.RF.3.3d Distinguish between similarly spelled words by identifying the sounds of the letters that differ. K.RF.4.4 Read emergent-reader texts with purpose and understanding.

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Many of the particles that surround Saturn come from active jets on the surface of its moon Enceladus. But NASA’s Cassini spacecraft was able to nab a few microscopic grains with much stranger origins. Scientists believe these unusual grains (and they were only about to get 36 of them) come from interstellar space—the huge swaths of relative emptiness between star systems. Unlike the majority of particles around Saturn, which are icy, Cassini’s Cosmic Dust Analyser determined that these were composed of minerals like silicon, calcium, and iron. Stranger still, they also did not resemble stardust grains found in some meteorites. The grains were moving at over 45,000 mph and on a path somewhat different from the other particles orbiting Saturn. While no less impressive, interstellar dust has been encountered by previous missions. NASA’s Galileo spacecraft was the first to observe alien particles, which were later determined to come from a gas and dust bubble which our solar system is travelling through called an interstellar cloud. Featured image: NASA/JPL-Caltech

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The above lesson includes audio (so remember to switch on your speakers). Use the play/ pause button if you need to stop and start the lesson. This fraction lesson is number 1 of 6 and introduces fractions with an illustrated discussion on their use and on how they are written and spoken using numerators and denominators. Related Fractions Lessons The Fractions Lesson explained above is aligned with the standard 3NF01 from the Common Core Standards For Mathematics (see the shortened extract below). The resources below are also aligned to this standard. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b Similar to the above listing, the resources below are aligned to related standards in the Common Core For Mathematics that together support the following learning outcome: Develop understanding of fractions as numbers

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Pre-unit diagnostic assessment Assess students’ ability to • use the Pythagorean Theorem to find unknown lengths in right triangles; • use properties of similar triangles to solve for an unknown side in similar right triangles. After an open-ended task intended to motivate the need for trigonometric ratios (although the term is not used), students examine side ratios of similar right triangles. Students then build tables of side ratios for several similar triangles while noting that quotients of corresponding sides are the same. Using their knowledge of similar triangles they see that the ratios are a property of an angle rather than of a triangle. Only after laying this groundwork do students learn that, for right triangles, the ratios are called “sine,” “cosine,” and “tangent.” Finally, students examine the relationship between sine and cosine and use this knowledge to solve a variety of problems.

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It's not important for National Curriculum Computing at KS3 that you understand how to create a program to draw a circle, but, if you're interested, here are two techniques explained. GCSE Maths now includes trigonometry and Pythagoras in both tiers, so these techniques should be suitable for students of GCSE Computer Science. GCSE Maths students will have been introduced to trigonometry - sines and cosines - for their Maths exam. If you don't know what sines and cosines are, or you would like a reminder of what they are, check out the animation here. This method of drawing a circle works by varying the angle n and using trigonometry to work out where the point (x,y) would be for that angle. As you could hopefully see from the animation, for a circle of radius 1, x would be cos(n) and y would be sin(n). For a larger circle, you just need to multiply by the radius. The program draws a circle of radius 400, so the x-coordinate is 400 x cos(n), and the y-coordinate is 400 x sin(n). There is, however, one slight complication. Unlike your calculator, most programming languages (and applications such as Excel) measure angles in radians, rather than degrees. The program therefore uses the RAD() function to convert the angle from degrees to radians before calculating the sine or cosine. You might find the Maths for this method more straightforward - and so does the computer! Square roots are quicker for the computer to calculate than sines and cosines, which explains why this method is quicker. Pythagoras works with right-angled triangles. Imagine a triangle with one corner in the centre of the circle, and another on the circumference. The hypotenuse (the longest side) will always be equal in length to the radius. This method of drawing the circle varies the x-position. From the x-position, we know the width of the triangle, and we know the length of the hypotenuse, so we can use Pythagoras to work out the height of the triangle to give us the y-position. If we assume that (0, 0) is in the middle of the circle, then the value of x is the width of the triangle - it might be negative, but as we're going to square it, it doesn't matter. If the hypotenuse is 400, then y2 = 4002 - x2, or y is the square root of (160000 - x2). If you would like to see how these techniques work in practice, watch the video on programming efficiency on the AdvancedICT YouTube channel.

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From the air, most of Greenland looks completely barren—a vast, frigid, inhospitable expanse of ice where nothing could possibly live. A closer look, however, shows that this isn’t true at all. The surface of the ice of Greenland is peppered with dark holes, ranging from a few inches to a few feet across, harboring self-contained micro-ecosystems that can host life in variety of different flavors, from red and green algae to cyanobacteria and the tiny organisms known as tardigrades and rotifers. These so-called cryoconite holes are remarkable enough in themselves—but they could also play a crucial role in our search for potential life on, of all places, Mars. To understand why takes a bit of explaining. Cryoconite itself is a mix of mineral dust, soot, ice algae, bacteria and other microorganisms that blows onto the icecap in Greenland and other frozen parts of the world; it was first described and named by the Finnish Arctic explorer Nils A. Nordenskiöld during his travels to Greenland in 1870. Because it’s dark and absorbs heat from the sun, cryoconite can accelerate the melting of the surface during summer. As the dark particles begin to coalesce, they can literally melt their way into the ice, creating cylindrical shaped holes that melt deeper and deeper as the sun warms their base until they’re too deep for sunlight to reach. Melting catalyzed by cryoconite can add to Greenland’s contribution to global sea-level rise. For this reason, there has been growing interest within the scientific community in understanding how biological and mineralogical materials absorb and reflect light at different frequencies (that is, different colors), with the ultimate goal of factoring these processes into the models that simulate current estimates and future projections of Greenland’s melting. Part of this work needs to be done on the ground: the spectral “fingerprints” collected on the surface can in theory be used in conjunction with satellite images to map the spatial and temporal evolution of cryoconite across wide swaths of territory from space. For obvious reasons, the more colors a satellite can collect within the electromagnetic spectrum, the more detailed its maps will be. It’s like the difference between a grainy or blurry photo and a sharp one. Sensors that collect data in a relatively small number of spectral bands (up to a few tens) are called multispectral, while those collecting hundreds of bands are called hyperspectralsensors. Multispectral data are routinely collected over our planet but cannot properly be used for mapping cryoconite over Greenland, at least not yet. The acquisition and use of hyperspectral data are still crucial. Unfortunately, there is currently no satellite with a hyperspectral sensor orbiting the Earth, and previous space-based hyperspectral sensors were “turned on” only for specific periods and over selected areas. Hence, despite the fact that we have now abundant and unprecedented measurements from the ground concerning spectral properties, we cannot benefit from them because of the paucity of spaceborne hyperspectral data. This problem has been recognized in the recently released 2018 Earth Science Decadal Survey, the goal of which is to help shape science priorities and guide NASA investments into the next decade. Collecting spectrally rich data over our home planet is not only going to unveil undiscovered secrets and crucial processes that can tell us how our ice sheets will respond to climate change. It can also offer a tool to decipher the alphabet of life on other planets, like a Rosetta stone that is under our eyes and it is just waiting to be discovered. Contrarily to what happens on Earth, hyperspectral data is very abundant over Mars. The spatial and temporal coverage, as well as the spectrally dense nature of the Mars dataset, offer a unique opportunity to explore potential signs of life, such as cryoconite-analog ecosystems, by merging ground-based data from Earth with space-based data from the Red Planet. The application of spectral fingerprints of cryoconite collected on Earth (now impossible to be collected on Mars) to the hyperspectral Mars data (not available on Earth) is not a new concept. Nevertheless, the data revolution that has occurred over the past few years offers a unique chance for a paradigmatic shift: today it is indeed possible to download and process huge volumes of data collected around Mars with a click on our laptops. Moreover, our knowledge of processes on Mars has improved dramatically, allowing scientists to produce high-quality, robust, spectrally dense satellite maps with the same quality as those over the Earth. And lastly, recent improvements of our understanding of the ice sheets and their processes has promoted and catalyzed a collection of datasets focusing on the hyperspectral properties of ice and snow algae, bacteria and other bio-ecological systems that is unprecedented. Continuing collecting in-situ data of cryoconite systems is, therefore, fundamental not only to studying the impact of biological activity on the potential sea level rise from Greenland but also to investigating the potential existence of life on Mars. By looking at our survival on this planet we also look into our chances to find places that other organisms already call home. At the same time, we need to be able to study our planet from space as well as we do the Red Planet. Let us remember that looking into the microscopic world of life that strives on the ice of our planet and understanding the impact of anthropogenic activity on the Earth’s climate is not only a duty for ethical, societal and economic reasons but also an area of research that could unveil the mysterious secrets of life.

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In 1926, famed astronomer Edwin Hubble developed his morphological classification scheme for galaxies. This method divided galaxies into three basic groups – Elliptical, Spiral and Lenticular – based on their shapes. Since then, astronomers have devoted considerable time and effort in an attempt to determine how galaxies have evolved over the course of billions of years to become these shapes. One of th most widely-accepted theories is that galaxies changed by merging, where smaller clouds of stars – bound by mutual gravity – came together, altering the size and shape of a galaxy over time. However, a new study by an international team of researchers has revealed that galaxies could actually assumed their modern shapes through the formation of new stars within their centers. The study, titled “Rotating Starburst Cores in Massive Galaxies at z = 2.5“, was recently published in the Astrophysical Journal Letters. Led by Ken-ichi Tadaki – a postdoctoral researcher with the Max Planck Institute for Extraterrestrial Physics and the National Astronomical Observatory of Japan (NAOJ) – the team conducted observations of distant galaxies in order to get a better understanding of galactic metamorphosis. This involved using ground-based telescopes to study 25 galaxies that were at a distance of about 11 billion light-years from Earth. At this distance, the team was seeing what these galaxies looked like 11 billion years ago, or roughly 3 billion years after the Big Bang. This early epoch coincides with a period of peak galaxy formation in the Universe, when the foundations of most galaxies were being formed. As Dr. Tadaki indicated in a NAOJ press release: “Massive elliptical galaxies are believed to be formed from collisions of disk galaxies. But, it is uncertain whether all the elliptical galaxies have experienced galaxy collision. There may be an alternative path.” Capturing the faint light of these distant galaxies was no easy task and the team needed three ground-based telescopes to resolve them properly. They began by using the NAOJ’s 8.2-m Subaru Telescope in Hawaii to pick out the 25 galaxies in this epoch. Then they targeted them for observations with the NASA/ESA Hubble Space Telescope (HST) and the Atacama Large Millimeter/submillimeter Array (ALMA) in Chile. Whereas the HST captured light from stars to discern the shape of the galaxies (as they existed 11 billion years ago), the ALMA array observed submillimeter waves emitted by the cold clouds of dust and gas – where new stars are being formed. By combining the two, they were able to complete a detailed picture of how these galaxies looked 11 billion years ago when their shapes were still evolving. What they found was rather telling. The HST images indicated that early galaxies were dominated by a disk component, as opposed to the central bulge feature we’ve come to associate with spiral and lenticular galaxies. Meanwhile, the ALMA images showed that there were massive reservoirs of gas and dust near the centers of these galaxies, which coincided with a very high rate of star formation. To rule out alternate possibility that this intense star formation was being caused by mergers, the team also used data from the European Southern Observatory’s Very Large Telescope (VLT) – located at the Paranal Observatory in Chile – to confirm that there were no indications of massive galaxy collisions taking place at the time. As Dr. Tadaki explained: “Here, we obtained firm evidence that dense galactic cores can be formed without galaxy collisions. They can also be formed by intense star formation in the heart of the galaxy.” These findings could lead astronomers to rethink their current theories about galactic evolution and howthey came to adopt features like a central bulge and spiral arms. It could also lead to a rethink of our models regarding cosmic evolution, not to mention the history of own galaxy. Who knows? It might even cause astronomers to rethink what might happen in a few billion years, when the Milky Way is set to collide with the Andromeda Galaxy. As always, the further we probe into the Universe, the more it reveals. With every revelation that does not fit our expectations, our hypotheses are forced to undergo revision.

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About 199 million years ago, on a small patch of land that is now preserved in the present-day African nation of Lesotho, there was an inclined slope next to a riverbed. Within hours, days, or even weeks of each other, several different dinosaurs climbed up and down the slope, leaving their footprints behind. Their tracks can still be seen there today, and as reported by paleontologists Jeffrey Wilson, Claudia Marsicano, and Roger Smith in the journal PLoS One, these tracks give us some clues as to how those dinosaurs moved. Dinosaur footprints are effectively bits of fossilized behavior, and the Lesotho tracksite provides a rare look at how dinosaurs walked when moving up or down inclines. The site preserves the tracks of several ornithischian dinosaurs, which may have been similar to Lesothosaurus, and a single theropod dinosaur, which the researchers compare to Dracovenator. They handled the slippy slope in different ways. The theropod dinosaur tracks show that it was walking parallel to the riverbank on the top of the slope before veering downwards to descend to the water. When it did so it stayed on two feet but it moved more slowly, as indicated by the shorter length between footprints in the portion where it was going downhill. This dinosaur also appears to have gripped into the ground with its foot claws, steadying itself as it moved downhill. The ornithischians did something different. One of the ornithischian dinosaurs started on the riverbank and moved up the slope, and as it moved it changed the way it walked. On the riverbed it walked on all fours, holding its limbs out to the side and placing its entire foot on the ground. This was a slow-and-steady posture. As it began to move up the slope, however, the dinosaur moved its limbs closer to the midline of the body and stood on its tiptoes. Only when it reached the top of the slope did the dinosaur then stand up on two legs, keeping the same tip-toed posture. What these tracks show is that the way dinosaurs handled walking on inclined surfaces was constrained by the type of bodies they had. The ornithischians changed their posture to cope with different obstacles and walked on all fours if they had to. The theropod, by constrast, could not do the same. It probably had arms that were too short to assist it in coming down the hill and thus relied on gripping the ground with its feet to stabilize itself. At a time when we regularly see dinosaurs walking around on television and in movies this might seem kind of humdrum, but I think this description is still impressive. It provides us with a fleeting glimpse into the lives on animals that have been dead for hundreds of millions of years.

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A Note About Units When dealing with gases and the gas laws, you will need to solve for, or plug into an equation, values for many different quantities. Paying attention to units is important. When dealing with volume, it is good practice to make sure your values are always in liters (L). Although you can sometimes get away with milliliters (mL), there are some situations where this is not the case. Therefore it is recommended that liters always be used. Temperatures must be converted to kelvin. The mathematical signficance of this is twofold and is related to the proportions often used to solve problems. First, the temperature variable is in the denominator of certain problem solving processes, meaning that plugging in a value of 0°C would imply that you are dividing by zero. Secondly, if you using a proportion and plug in a negative Celsius temperature into one ratio and a positive temperature into the other, you will end up with a negative propotion equalling a positive proportion. To eliminate the mathematical impossibilities, always use absolute (kelvin) temperature. Boyle's Law is an expression of the relationship between the pressure and volume of a fixed quantity of gas. It was initially described by Robert Boyle in the 17th century. - Temperature and moles of gas are constant - Graph is hyperbolic (see below) and asymptotic to both axes - Pressure and volume are inversely proportional to each other Problems that require you to use Boyle's Law will only mention pressure and volume. Do not get fooled if the phrase "constant temperature" is used. This means that temperature remains constant and is irrelevant to the mathematics of the problem. An example problem may read: Find the pressure on 5.25 L of gas that was originally 3.12 L at 1.54 atm. In this problem, a preliminary conversion of units will not be necessary unless the problem explicitly asks for a unit that is different than that given in the problem. Refer to the Boyle's law equation above. Set aside P1 and V1 for the initial conditions of the gas. V2 will be for the new volume of the gas and P2 will be what we solve for: - Pressure and moles of gas are constant - Graph is linear (see below) - Volume and temperature are directly proportional to each other It's important to remember that temperature must be converted to kelvin when utilizing any of the gas laws. Since thermometers are designed to use degrees Celsius, lab data or values given in a problem will likely need a conversion. Note that in the example problem below, nothing is said about pressure: A 5.0 L vessel of gas is held at 25°C. What will be the new volume if the temperature is doubled? Do not be fooled into thinking that since the temperature doubles, so does the volume. That would be true if the kelvin temperature doubled, but the Celsius temperature doubling from 25 to 50°C is not a significant increase: - Volume and moles of gas are constant - Graph is linear (see below) - Pressure and temperature are directly proportional to each other Consider the following problem as an example: 25.0 L of a gas is held in a fixed container at 1.25 atm at 20°C. What will be the pressure of the gas if the temperature is increased to 35°C? First, the temperatures must be converted to kelvin: Next, the appropriate subsitutions can be made into the equation. Note that the volume given in the problem is immaterial to the solution. The phrase "fixed volume" communicates that volume is constant in this problem, and thus any equation that uses "V" is not to be used. Combined Gas Law The combined gas law integrates Boyle, Charles, and Gay-Lussac's laws. Here, the only constant is the number of moles of gas. Notice that if you cover on set of variables, either Charles, Boyle, or Gay-Lussac's Law remains. For example, if you cover T1 and T2, the remaining equation is the same as Boyle's Law. Removing P1 and P2 leaves Charles's Law and eliminating V1 and V2 leaves Gay-Lussac's Law. Ideal Gas Law The ideal gas law is used to approximate the behavior of a gas at conditions given by the pressure, temperature, and volume variables. Typically, the approximation is reasonable for situations close to STP (1 atm pressure/273.15 K), but deviates greatly at extreme pressures and temperatures. Unlike the previously mentioned gas laws, there is no "initial" and "final" or "before/after" context to a problem that uses this law. Generally, this law is utilized for gas stoichiometry problems or situations where most conditions of a gas are known except for one. Let's look at a problem that involves the second scenario. While there are five variables in the ideal gas law, one of them is the gas law constant R. It is not going to be a variable you will ever solve for, but it is a constant whose value - 0.0821 L × atm × mol-1 × K-1 - will always be plugged in for R. The unit for R looks intimidating but it is only that long because it incorporates the units of the other four variables in the problem: pressure, volume, moles, and temperature. Be aware that the unit for R dictates that any temperature substituted for T must be kelvin and any pressure substituted for P must be in atm. Consider the following problem: Determine the volume of 45.9 g of neon gas at 78.2°C and 184 kPa pressure. First, we know the ideal gas law must be used here because a pressure, temperature, and mass (which can be easily converted to moles) are given. Additionally, the problem asks for volume to be determined. Since P, V, n, and T are all present, the ideal gas law is the only option. Next, make sure that any values given are in the necessary units. As will often be the case, conversions will be necessary: Now that all the conversions have been made, substitutions into the equation can be made: Dalton's Law of Partial Pressures Like the ideal gas law, Dalton's law makes some key assumptions. Namely, the gases must be unreactive and follow ideal gas behavior. The law says that the total pressure of a gas mixture is equal to the sum of the pressures of each individual gas. Density of Gases In the derivation below, M represents the molar mass for the particular gas and m represents the mass of the gas sample. Note that unlike Boyle's, Charles's, or Gay-Lussac's Law, the identity of the gas makes a difference when determining density, but ultimately the mass of the sample does not. The initial substitution of n (moles) for m/M reflects how the number of moles of a substance is calculated - from dividing mass by molar mass. Densities of liquids and solids are typicalls expressed in g/mL or g/cm3. However, since a mL of gas would contain a very small amount of mass, the denisty of a gas is generally expressed in g/L. Van der Waals Constants The van der Waals constants for a gas are used when the ideal gas law is not going to give a good approximation. This happens the further one deviates from STP, and with an increased presence of intermolecular forces between particles of a gas. The van der Waals equation is given below: This can be seen as a modification of the ideal gas law, notably with the addition of variables "a" and "b." These variables are unique for each gas and provide a calculation that is more representative (but still not always correct) of a gas at the conditions plugged in for pressure, volume, or temperature. When dealing with gases, it is often more important to know the volume of gas that is produced during a reaction than its mass. At STP, 1 mole of any gas will occupy a volume of 22.414 L. This is an important stoichiometric relationship, but it is only useful at STP. At non-STP conditions, the ideal gas law must be utilized. See the stoichiometry page for more detail.

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English is a complex language with several pronunciation rules dependent on word length, vowel and consonant placement and the context in which a particular word is used. Some rules are definitive, such as the requirement of every English word to have a vowel.Continue Reading There are basic guidelines for consonants and vowels that are helpful for understanding how to pronounce words. The English language has five vowels: a, e, i, o and u. For words that only have consonants such as "dry" or "why," the letter "y" acts as a vowel. The rules for consonant pronunciation tend to be more situational. For instance, the letter "b" is typically pronounced with a long sound at the beginning of a word, like "bear" or "bond." However, for words that end in the letter "b" such as "climb," the "b" is silent. Each English word also has a certain number of syllables that dictate the pace at which the word is pronounced. Generally, the number of syllables in a word is equivalent to the number of vowel sounds heard when the word is vocalized. The recommended method to properly learn the rules of English pronunciation is to consistently practice by communicating with English speakers.Learn more about Education

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The Characteristics of: 1. Drawing on knowledge and applying it to new situations. Means to teach students how to apply school-based knowledge to real-life situations. One example of using this in my classroom would be when I have my students perform character interviews. Not only do they have to practice communication skills, but they have to take on the role of a different person other than themselves in a mock interview in front of the class. This also prepares them for communicating during job interviews and meetings. 2. Creating, Imagining, and Innovating. Means to teach students the value of feedback. One example of using this in my classroom would be when my students critique each others' performances. They give each other 2 stars (2 things they think that person did well) and 2 wishes (2 things they think the person could improve). Students then rehearse with the improvements they have made based on the class critiques. 3. Responding with wonderment and awe and thinking interdependently. Means that teachers encourage students with "I can" and help them to have a sense of "I enjoy" when they are working on an assignment. One example of using this in my classroom would be when I have 8th grade students create their own scripted scene. They have to create their own storyline and script. They also must decide what each person's role is within the group (actor, crew, costume, director,etc.) This gives students an idea of "I can" and they usually enjoy creating their own scenes. 4. Using all the senses. Means to have students use all their sensory input channels (verbal, visual, tactile, and kinesthetic) In theatre, we are constantly using all of our senses. For example, we write scenes, act, choreograph dances, practice stage combat, design sets, etc. 5. Thinking flexibly. Means that students approach a problem from a new angle. They learn from different points of view. I practice this characteristic in multiple ways in my classroom. One example is when students take on a character on stage. They must first research that character. They have to know the character's background and what their motivation is. They have to be able to take on the character's point of view. Students also practice this characteristic when they work in scene groups with each other. Sometimes, they all have different points of view of the scene or the set and they have to discuss each point of view and decide what will work for the group as a whole.

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An earthquake occurs when massive rock layers slide past each other. This motion makes enormous vibrations, which travel from the site of the earthquake in waves. The waves (seismic waves) travel all the way through the Earth. Seismologists can record these waves when they reach Earth’s surface using seismographs. Earthquakes generate three kinds of waves: Compressional waves (P waves) travel the fastest. Shear (S) waves travel more slowly than P waves. Surface waves are the slowest of the three. - Two Slinkys™ - Flat, smooth surface - Notebook and pen - Safety goggles - Work with a partner. Put on safety goggles before starting this activity. With a partner, stretch out a Slinky™ on the floor about as far as it can go without making a permanent bend in the metal. - Have one partner make waves by gathering several coils at the end of the Slinky™ and then releasing the coils, while still keeping hold of the end of the Slinky™. Observe the direction of wave movement relative to the Slinky™. Does it move in the same direction (parallel to the Slinky™) or in the opposite direction (perpendicular to the Slinky™)? Record your observations. - This kind of wave is called a P (primary) or compressional wave. (To compress means to squeeze together.) From your observations, explain why this is a good name for this wave. You may wish to use diagrams to illustrate your answer. - Stretch out the Slinky™ again. This time, have one partner make waves by moving the Slinky™ from side to side (left to right or right to left). Again observe the direction of wave movement, relative to the Slinky™. Does the wave move in the same direction (parallel to the Slinky™) or in the opposite direction (perpendicular to the Slinky™)? Record your observations. - This kind of wave is called a secondary or shear (S) wave. (To shear means to slide one thing sideways past another thing.) From your observations, explain why this is a good name for this wave. - Stretch out the Slinky™ a third time. This time, move one end of the Slinky™ up and down to generate a wave. This shows how the surface waves from earthquakes behave. What effect could this type of wave have on houses anchored to the Earth’s surface? Why is that? NGSS 3-D Learning - Science and Engineering Practices ─ Developing and Using Models - Disciplinary Core Ideas ─ Earth’s Systems - Crosscutting Concepts ─ Cause and Effect

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It was roughly six years ago – back in 2011 – that a magnitude-9 earthquake triggered a catastrophic tsunami, which devastated areas of northeastern Japan. You may recall the subsequent headlines, many of which focused on the resulting Fukushima Daiichi Nuclear Power Plant meltdown. It’s scary to think that this disaster was neither the largest nor deadliest earthquake-tsunami combo in history. And that grim point is one reason a team from the Japan Agency for Marine-Earth Science and Technology Kochi Institute is looking for ways to mitigate the size of tsunamis. What's possibly most interesting about the institute’s recent tsunami research, though, is that they’ve been investigating how to use bacteria to stifle tsunami size. That’s right - bacteria. The team behind this mitigation moonshot pictures a future in which bacterial secretions can be scaled and used to fill the gaps between tectonic plates. The idea is to minimize the size of the tectonic shifts in order to reduce the severity of potential earthquakes and consequent tsunamis. (By the way, if you aren’t familiar with the science behind tsunamis, you can check out this awesome TED Ed animated video explanation). Before designing the bacterial approach to tsunami deterrence, researchers at the Kochi Institute played with the idea of using a substance similar to cement to connect tectonic plate boundaries. Unfortunately, this approach fell short when the team had trouble getting the sticky substance to spread out. That’s when they pivoted to the idea of using carbonate ions, which are secreted by certain types of bacteria, and can form calcium carbonate when exposed to calcium in sea water. Calcium carbonate is cement-like so it has the potential to create the friction necessary to impede tsunamis. From certain logistical standpoints, the bacteria make sense given that they are self-reproducing and can fit into the spaces between tectonic plates. When researchers put a calcium carbonate-producing strain of bacteria, known as Sporosarcina ureae, in conditions similar to those experienced at fault lines, they found the bacteria were able to increase friction by nearly 10 percent. Getting meaningful quantities of these bacteria to plate boundaries remains a significant challenge, and there are environmental considerations to be made; however, the researchers’ results show that this moonshot is off to a promising start.

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Any video from this channel has a great experiment, which I can use to get the students to write a procedure, as each step is printed on the screen. The demonstrator also emphasises safety and spells out how he is doing the experiment. So, at the start of year 7 your students should be able to write a procedure from a source such as this then hopefully discuss what happened. I do use examples that allow me to talk about the science, such as density, air pressure or solubility but if you used an example like this one K-6 , just to discuss variables and fair tests as per your syllabus: 1. Students watch youtube to write a procedure, using numbered steps and correct text type 2. students discuss what experiment they could test based on this experiment, perhaps give them the equipment you have such as 2 liquids and corn. You could get some great discussion to get students to make up their own hypothesis. Then I'm sure you get them to suggest one experiment such as that the corn kernel will float in the maple syrup by not water. 3. Students write one hypothesis eg corn will float is thick liquids ( like maple syrup) but not thinner liquids (like water) Now you have the basis of an investigation, because you can change ONE THING ie the liquid the corn gets floated in and test one thing. To a scientist the one one you changed is the independent variable . You test what floated so this is called the dependent variable. So "Does the kernel float?" Your answer depends on the liquid tested. Now what do we keep the same ?? The temperatures of the liquid, the amount of shaking, not stirring it. This is all about doing a FAIR TEST. so brain storm "How could we cheat??" Deliberately mix one? Change the size of the corn, or use 2 different objects? Students should realise that to be a fair test they have to treat each test the same except for the one thing they are deliberately changing. 3. Identify the variables you would have to keep the same to do a fair test. 4. What one thing are you changing and what are you testing? This is what we would have in year 7: Aim: to see which liquid the corn kernel will float in. Hypothesis the corn will float in thicker liquid like maple syrup but not thinner liquid like water Method 1. Get 100ml of each liquid in a beaker 2. Carefully place one corn kernel on the top of the liquid to see if it floats Controlled variables; size of corn, amount of liquid, temperature of liquid, no amount of stirring. table of results Relating to syllabus; Let's say you did this kind of experiment with your students at this stage, here what I think you'd end up with, just looking at one lot of outcomes. • show that equipment should be used with care and safety. ie wash hands after, don't eat etc • state the purpose of an investigation. To see what liquids the corn will float in • give examples of the ways the different senses can be used in observing. using eyes, perhaps also need magnifying glass• recognise that discoveries can be made through play, exploring and experimenting. experiment as shown on youtube and their simple version • demonstrate that tools and equipment can be used to aid observation. measuring height of liquid in a cup eg 2cm so its all the same get students to try to repeat part of the experiment with 2 liquids and corn, perhaps modifying design so the corn floats, using pencils etc to help make the corn floatStage Two • demonstrate that investigation can take many forms. ie testing floating • recognise that the results of investigations can lead to more questions. ie why does it not float in water. • show that designing and making can lead to the need for investigations.ie fair test • give examples of predictions that are sometimes supported, sometimes disproved. Write a prediction such as which liquid the corn will float in, or other liquids that it could float in. • recognise that investigations may be conclusive/inconclusive. test other liquids, or it doesn't always work • describe the social, environmental or economic implications of the investigation of new materials and processes. Such as using floatation in industry eg mining • identify investigations which involve discoveries leading to unexpected outcomes. possible use of this?? • show some relationship between the process of investigation and the process of designing and making. the need to change design if corn always sinks • describe the process of investigation which can involve exploring and discovering phenomena and events, proposing explanations, initiating investigations, predicting outcomes, testing, modifying and applying understanding. keep a journal of how they changed the stimulus material to what they actually did in class And looking at the other outcomes, you can see that there could easily be scope to meet those outcomes using this or similar experiment. For instance this for stage 3 • make detailed observations using appropriate technologies. photos, using a ruler to measure height of corn • discuss the factors that might affect an investigation.ie control variables • devise fair tests. is follow correct scientific procedure!!! • identify data which support a particular prediction.results , hopefully in a table • devise a test that will support or disprove a prediction.experiment • modify and apply their understanding in the light of their investigation. What they conclude about their experiment

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“No self-respecting woman should wish or work for the success of a party that ignores her sex.”— Susan B. Anthony, 1872 By the late 1800s, women in America and England—tired of being treated as second-class citizens by their societies and governments—were fed up. They began to fight back, particularly in pursuit of women’s suffrage. The organized women’s rights movement began in the United States in 1848, when the first Women’s Right’s Convention—led by Elizabeth Cady Stanton and others—was held in Seneca Falls, N.Y. Many women were excluded from other reform efforts of the day, such as the abolition and temperance movements, and they often were refused seating or ejected from anti-slavery conventions—purely because of gender. Men and women began to work side by side for both abolition and women’s rights, and after the Civil War the Equal Rights Association was established. The pressure for reform led to passage of the 13th and 14th Amendments (in 1865 and 1868, respectively), ending slavery and granting citizenship to African Americans. The right to vote, however, was still an issue. Many women assumed they would be granted voting rights alongside African Americans, but the 15th Amendment—ratified in 1870—prohibited governmental infringement of a citizen’s right to vote “on account of race, color, or previous condition of servitude.” The question of gender was ignored. The Equal Rights Association had split in 1869, and out of the wreckage came two rival groups. Stanton and Susan B. Anthony formed the radical National Woman Suffrage Association in 1870, and other women’s rights crusaders established the more moderate American Woman Suffrage Association. Both groups worked throughout the country distributing pamphlets, giving speeches and presentations to women’s clubs, and campaigning for support from individual states. The National Woman Suffrage Association also lobbied Congress, but the question of suffrage was proposed only once in congressional hearings, and it failed. By 1890, many more women had joined the cause, and the two organizations decided to put aside their differences and create a single group. The new organization, the National American Woman Suffrage Association (NAWSA), retained the leadership of Stanton and Anthony. The new century saw the U.S. suffrage movement shift to a more dramatic and militant strategy. Under Anthony’s rallying cry of “Failure is impossible!” suffragettes employed publicity campaigns, civil disobedience, and nonviolent confrontations as tactics. This approach was influenced by and modeled on the activities of British suffragettes, who were crusading for women’s rights on the other side of the Atlantic. In England, the charismatic Emmeline Pankhurst and her daughters Christabel and Sylvia were leading the fight for suffrage. In 1903, they founded the Women’s Social and Political Union (WSPU), the first and largest militant suffrage organization in England. Their initial campaigns included demonstrations and peaceful confrontations, but when those efforts proved fruitless, they chose more radical methods. In 1908 they began breaking the windows of government buildings and even threw stones through the windows of the Prime Minister’s home. At one demonstration in London, the WSPU incited the public to “rush” the House of Commons, resulting in a violent clash with police. This event and others culminated in the arrests of many women, quite a few of whom went on hunger strikes in prison and were force-fed by the authorities. Emmeline Pankhurst endured 10 hunger strikes over an 18-month period and nearly died in the process. The WSPU’s militant tactics continued to escalate, and by 1914 more than 1,000 women had been imprisoned for arson or destruction of public property. They suffered harsh treatment at the hands of their jailers, and many were beaten. With the onset of World War I, the WSPU suspended all political activity and began negotiations with the British government. The organization agreed to end its militant campaigns and help with the war effort, and in return, the government released all suffragettes from prison. In the United States, the fight continued, and Carrie Chapman Catt and Alice Paul emerged as new leaders. Catt took over NAWSA after Anthony’s retirement in 1900, and though she left office after four years to care for her dying husband, she came back to the movement as leader of the New York State suffrage campaign. She returned to head NAWSA in 1915. Alice Paul was introduced to the English suffragist movement as a student at the London School of Economics and was one of the militants arrested and force-fed in jail. Upon her return to the United States she coaxed NAWSA into letting her organize a lobbying arm in Washington, D.C. Paul also planned one of the most influential events of the American suffrage movement, an elaborate political parade held the day before Woodrow Wilson’s inauguration in March 1913. She organized 8,000 college, professional, working-class, and middle-class members of NAWSA into marching units—complete with suffrage floats—that paraded down Pennsylvania Avenue, starting at the Capitol and moving past the White House. A suffragette astride a white horse and dressed in white robes led the procession—a Joan of Arc figure symbolizing righteous women fighting for a moral cause. The mostly male crowd of parade watchers taunted, spit on, and physically abused the marchers, disrupting the event. Police did little to protect the suffragettes, and the U.S. War Department called in the cavalry to prevent a riot. Since many of the marchers and their supporters were members of the political and social upper classes, the incident embarrassed the new administration. Congress began hearings into the police department’s mishandling of the situation, but the damage was done. Headlines appeared across the country giving women’s suffrage enormous publicity and effectively granting the movement major political status. Paul continued her public demonstrations, organizing pickets and publicly burning the speeches of President Wilson in front of the White House. Many American women were arrested during these demonstrations and endured the same abuse suffered by the English suffragettes. But as time passed, public opinion in both countries began to favor the suffragettes. In America many Western states—with more progressive, frontier-influenced views about women—granted voting rights to women, and in 1917 New York State approved women’s suffrage. Three years later the 19th Amendment was passed, proclaiming that the right to vote “shall not be denied or abridged by the United States or by any State on account of sex.” England granted the vote to women age 30 and older in 1918, but it was another 10 years before English women were granted full and equal voting rights.

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With the promise of freedom and new economic and educational opportunities, Kansas attracted many African Americans in its territorial days, through statehood, and into the 20th century. Slavery existed in the Kansas Territory, but slave holdings were small compared to the South. Many black migrants also came to the territory as hired laborers, while some traveled as escaped slaves through the Underground Railroad. In the 1860s, others joined the Union Army, and some moved from the South in large groups during the Kansas Exodus, a mass migration of freedpeople during the 1870s and 1880s. As a territory that had a long and violent history of pre-Civil War contests over slavery, Kansas emerged as the “quintessential free state” and seemed like a promised land for African Americans who searched for what they called a “New Canaan.” Slavery in Antebellum Kansas and the Underground Railroad Although there were relatively few slaves in territorial Kansas, enslaved men and women provided important labor along the Missouri-Kansas border. Unlike large plantations in the South, slavery in the border region existed in small holdings, permitted closer contact between slaves and slaveholders, and allowed slaves to hire themselves out with the permission of owners. The issue of slavery’s expansion into the West turned Kansas into a battleground as it prepared to enter the Union. A bill passed in 1860 would abolish slavery in Kansas, but before then, antislavery settlers campaigned against proslavery factions. Abolitionists raised money for fugitives through aid societies and publicly argued against slavery on lecture circuits. Daniel Anthony, the brother of woman suffragist Susan B. Anthony, moved to Kansas in 1854 with the Massachusetts Emigrant Aid Society for the express purpose of fighting against the extension of slavery into the territory. Antislavery activities could be as violent and sporadic as John Brown’s vigilante raids on proslavery neighbors, or they could be more cautious and systematic, as were the secret Underground Railroad “stations” meant to shuttle escaped slaves to freedom. The Underground Railroad was not actually a train, but rather a large, national network intended to help fugitives escape from slavery into northern states and Canada. White and African American abolitionists created a large but informal network of hiding places in farmhouses and in the woods throughout the South, so that conductors could help passengers travel from station to station under the cover of night. Fugitive slaves and those who aided them risked their own safety, especially after the 1850 Fugitive Slave Act required the return of runaway slaves to their owners even if they had made it into a free state or territory. A 19th century minister once claimed that the number of escaped slaves who passed through his town of Lawrence, Kansas, amounted to $100,000 worth of property during the territorial period. Depots in Kansas proved to be especially important to fugitive slaves from Missouri en route to Nebraska, Iowa, and even Canada. Quindaro residents established several Underground Railroad stations, where many African American slaves sought refuge on their way to freedom. In some cases, abolitionists established new towns near the Missouri-Kansas border to reinforce the “cause of liberty.” An example of such a town is Quindaro, located in present-day Kansas City, Kansas. The name, Quindaro, was a Wyandotte word meaning “bundle of sticks,” which evoked an ideal of strength in unity. The town, founded in 1856, quickly grew because of its port near the confluence of the Kansas and Missouri rivers, as well as its subsequent establishment of surveyors, businesses, and stone and brick yards. The boom of Quindaro’s first year did not sustain the community for long, though, and by 1862 the state legislature had taken measures that led to the voiding of the town’s incorporation. However, during its existence, Quindaro residents established several Underground Railroad stations, where many African American slaves sought refuge on their way to freedom. An example of a frequently used station was Quindaro’s high school for African Americans, established by a white minister, Eben Blatchley, in 1857. In 1865, Blatchley named the school Freedmen’s University, and in 1881 it was finally renamed Western University, with the sponsorship of the African Methodist Episcopal Church. The school lasted much longer than the town, gaining support from local communities and the state legislature and earning a reputation as a school where African American students could excel academically until its closure in 1943. The Underground Railroad activities at Blatchley’s school maintained secrecy during the antebellum period, but in 1911, the school and the Quindaro community created a public reminder of its anti-slavery stance by installing a life-size statue of John Brown. For his leadership in a failed insurrection of slaves, Brown had been charged with treason and hanged for his attempt to start a slave insurrection at Harpers Ferry in 1859. The statue of the martyred hero stood in the front lawn of the school with a dedication: “Erected to the memory of John Brown by a grateful people.” War and Increased Demands for Education As skirmishes increased in Kansas in the years before the Civil War, so did a military buildup that included both whites and African Americans. Black soldiers joined Union troops as early as 1862 in the First Kansas Colored Infantry in the town of Fort Scott. Earning the distinction as the first African Americans engaged in Civil War battles, their initial combat took place at the Battle of Island Mound in Bates County, Missouri, in October 1862, even though the troops were not officially recognized by the federal army until a few months later. For some, joining the military also increased their chances with literacy in an era when it was otherwise illegal in many states to teach slaves how to read. Both escaped slaves and freedmen joined the Union Army because it ensured a certain amount of freedom for African American soldiers. For some, joining the military also increased their chances with literacy in an era when it was otherwise illegal in many states to teach slaves how to read. While in camp, soldiers would share each other’s letters and teach each other how to read the Bible. In 1865, when soldiers in the First Kansas Colored Infantry gathered their families to settle in Fort Scott, the Northwestern Freedmen's Aid Commission constructed a schoolhouse behind the officers' quarters of the military fort. At one point, the school served 160 children during the day and 75 adults in the evening. Eventually the legislature would levy taxes on property owned by African Americans to be appropriated for such schools, but until then local communities and aid societies maintained black schools. Most schools for African Americans were separate from white schools, but since the territorial legislature had ordered that schools should be available without charge for all children between the ages of five and 21 years, a certain commitment to African American education remained. By the end of the 1880s, Fort Scott had opened an additional school for children of African American Union soldiers. By 1956, Fort Scott had opened a total of four schools for black students, including one that the inventor George Washington Carver briefly attended as a teenager. As more African Americans migrated to Kansas after the Civil War, the demand for education also increased. Federal assistance, however, did not. The Bureau of Refugees, Freedmen, and Abandoned Lands, a branch of the War Department in the federal government, had opened in March 1865 with the purpose of supervising relief activities for refugees and freedpeople. The efforts of the Freedmen’s Bureau included providing medicine, land, rations of clothing and food, and education, as well as providing overall support for African Americans’ transition from slavery to freedom. The existence of the Freedmen’s Bureau was threatened by President Andrew Johnson, whose second veto of its renewal and expansion in 1866 was overturned by Congress. Although the Freedmen’s Bureau continued until 1872, its funding was significantly cut by 1869 and its operations were mostly suspended. Therefore, without much federal assistance, African Americans were left to depend on each other, on white reformers, and on small organizations to fund their schools. As African American populations increased in towns such as Lawrence, Topeka, Leavenworth, and Tonganoxie, Kansas-based charity organizations also demanded that public school districts assume more responsibility for African American schools. In general, white Kansans supported state and municipal legislation to fund African American education, although they did not necessarily call for the integration of public schools. Black students would continue to attend separate (although undoubtedly unequal) schools as long as the 1896 Plessy v. Ferguson United States Supreme Court decision upheld the legality of segregation. In Leavenworth, for example, African Americans had their own school, but some described it as a “hut” situated in a “low, dirty-looking hollow close to a stinking old muddy creek, with a railroad running almost directly over the building.” Despite such conditions and because of the voracious appetite for education among African Americans, civil rights organizations chipped away at Jim Crow laws that segregated white and black school children. Lawyers took 11 desegregation cases through courts of appeal up to the Kansas Supreme Court until Brown v. Board of Education of Topeka, Kansas finally went to the United States Supreme Court in 1954. The Supreme Court unanimously decided against “separate but equal” policies of the past and called for the eventual integration of public spaces, including schools. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License Butchart, Ronald E. Schooling the Freed People: Teaching, Learning, and the Struggle for Black Freedom, 1861-1876. Chapel Hill: University of North Carolina Press, 2010. Cox, Thomas. Blacks in Topeka, Kansas: 1865-1915, A Social History. Baton Rouge: Louisiana State University, 1982. Epps, Kristen K. "Bound Together: Masters and Slaves on the Kansas-Missouri Border, 1825-1865." Dissertation: University of Kansas, 2010. Kluger, Richard. Simple Justice. New York: Random House, Inc., 1975. Painter, Nell Irvin. Exodusters: Black Migration to Kansas After Reconstruction. New York: Alfred A. Knopf, 1976. Warren, Kim Cary. The Quest for Citizenship: African American and Native American Education in Kansas, 1880-1935. Chapel Hill: University of North Carolina Press, 2010. Williams, Heather Andrea. Self-Taught: African American Education in Slavery and Freedom. Chapel Hill: University of North Carolina Press, 2005.

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Students delve deeper into the concept of recycling and key issues such as ‘contamination’ and their responsibilities as a recycler at home are reinforced. By investigating product lifecycles students are able to see how they can have a positive impact on the sustainable use of natural resources by recycling. Children also discover what actually happens to their recycling after it leaves their house, from recycling bin to new end product Composting is a topic that deserves its own comprehensive unit and is a key tool in tackling our growing waste problem. Children investigate the role of nature in turning organic waste in to new compost. The key composting elements of nitrogens and carbons are examined and the differences between landfills and composts are explored. Children will build their own ‘mini-compost’ (containing tiger worms), giving them the skills and knowledge to build and maintain large-scale composts at home. All units are supported by workbooks / worksheets, interactive games and activities, DVD’s, relevant photos and website references

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This week we learned how to multiply ugly fractions, which is almost exactly the same as what we were taught around middle school except with a few more extra steps. For this question factoring any numerator or denominator possible will help simplify the question. In the second line we noticed that there were matching terms on the numerator and denominator, and by following the rules of fractions anything over itself is equal to 1, because there’s no point to multiplying by 1 we’re able to just cross out the matching terms leaving us with what ever is left over as our simplified fraction. This week we learned how to simplify “ugly” fractions. These are basically fractions that will involve factoring. A way to make these questions simpler is by crossing out common factors in the denominator and numerator of the fraction. The rule that anything divided by itself is equivalent to 1 still applies to these fraction, with that being said, by crossing out the common factors on the top and bottom of the fraction it shortens the question to it’s simplest form. We also learned that it is important to know the non-permissible values of x in the denominator. It is important to know because our denominator can never equal 0. therefore the non-permissible values of this expression are -5 and -8. This week he learned how to graph reciprocal quadratic functions. When beginning these questions it is always easiest to start by graphing the original equation, in this example it is x squared minus 3. After graphing this draw a broken vertical line on the zeros or x-intercepts, because this graph has 2 solutions it will have 3 hyperbolas. The 2 “L” shaped hyperbolas hover right above the x-axis and almost touching the broken lines. The hyperbola on the bottom follows the same rules except it’s on the other side of the broken line.

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Most bats are nocturnal, meaning they’re active at night and sleep during the day – opposite to our typical human lifestyle (Fig. 1). This nocturnal schedule is thought to be a strategy bats have evolved to take advantage of the many delicious insects (their prey) flying around at night. However, in order to reap the food rewards and deem this nocturnal lifestyle adaptive, bats must be able to efficiently and effectively hunt and catch these tiny, fast-moving insects. Foraging at nighttime is challenging, because it’s dark – this makes it both hard to see prey and easy to accidentally fly into a tree. So how do bats navigate, orient, and hunt in the dark? Nature has come up with a solution, and it’s a fascinating system that we’ll explore here. Figure 1. The a) Townsend’s big-eared bat (Corynorhinus townsendii) and b) White-winged vampire bat (*Diaemus youngi) *show off their highly adapted ears used to detect sounds relevant for communication, hunting, and navigation in the dark. (Photographs modified from Wikimedia Commons: (a) & (b).) Echolocation is a process in which bats produce sounds and then listen for the echoes of those sounds to return to them after bouncing off of objects (Fig. 2). Both the production of these sounds (emitted vocalizations) and the reception of these sounds (reflected echoes) are highly specialized so that bats can receive precise information about their surrounding environment based on the timing and intensity of these echoes. Essentially, bats are able to create an ‘acoustic map’ of the objects around them, using sound to understand where a tree branch, cave entrance, water source, or tasty insect might be located. They can accomplish this with similar acuity to what we humans achieve through sight, and this ‘acoustic map’ can then inform their behavior and movement decisions . Figure 2. This schematic shows how sound waves emitted from a bat’s echolocation call can move through the air, bounce off of a prey item, and reflect back such that they can be detected by the bat. (Diagram via Wikimedia Commons.) It’s difficult for us to imagine how this might work, because we don’t inherently use our own vocal and auditory abilities to echolocate (although as humans, we do have the capacity to train ourselves to do this to some degree – an ability particularly utilized and developed by some members of the blind community). But in a very rough way, we can understand the phenomenon by thinking about how our voices sound in, say, a tiny closet versus a large auditorium. In a tiny closet, the space is considered ‘dead’, with no reverberation. In a large auditorium, the space is considered ‘live’, with high reverberation. These distinct resonance qualities result from the different ways the sound waves from our voices reflect off of the room surfaces; both the size of the room (i.e. distance the sound waves travel before hitting a wall and bouncing back) and the structural materials (i.e. whether the sound waves are absorbed or reflected) affect the echoes. Imagine you were blindfolded and had to listen to your own echo to determine your whereabouts and identify the structures (or lack thereof) around you – in this scenario, you’d be echolocating! Most bats can do this with far better spatial resolution than we can, as it is their primary means of finding food and avoiding dangerous collisions. Because these objectives are fundamental to survival, behaviors (i.e. vocalizing) and morphological structures (i.e. ears) related to echolocation are subject to strong natural selection. For instance, bats with ears that enable awesome hearing will likely catch more insects, live longer, and pass on genes for awesome-hearing-enabling-ears to more offspring than those bats with not-so-helpful ears. Over time, bat populations should therefore evolve better and better hearing via better and better ear structures. This is an example of evolution through natural selection, and it helps explain why we see special adaptations for echolocation in modern bats. Many bat species today have large, mobile external ears that can move dynamically to enhance the detection of echoes in particular directions, allowing for precise localization of prey – in other words, awesome hearing (Fig. 1) . Echolocating bats use a range of specific sounds, or calls, adapted to specific circumstances. Some call types are best for scanning to locate prey while others are better for tracking and closing in on a known prey item. The utility of a certain call type is determined by the acoustic properties of different sound structures under different environmental conditions. Bats can even manipulate the pattern, tempo, and frequency of their calls during flight so that they can best capture relevant environmental features in real time – whether targeting tiny, moving prey items or searching for a large cave entrance. For example. as bats close in on prey targets, they speed up their vocalizing rate so that they are calling really fast, getting quick feedback to accurately pinpoint and capture the moving insect . Echolocation requires very specific sound production and perception capabilities, as well as the brain capacity to quickly process and integrate auditory information so as to inform suitable behavioral responses. This adaptive ability of bats to accurately interpret their environmental surroundings using sound is a truly fascinating biological phenomenon – and it even inspires applications for human industrial use. In fact, this natural echolocation system is so efficient and effective that some advances in our military and industrial sonar technology come out of our scientific discoveries around how bats echolocate and navigate with such precision and acuity . Recent investigations into how dense groups of bats avoid crashing into each other are inspiring the development of crash avoidance technology for drones and other unmanned aerial systems . Sometimes, nature knows best! James A. Simmons. “Perception of echo phase information in bat sonar,” Science 204 (1979): 1336-1338, accessed February 12, 2017, doi: 10.1126/science.451543. Melville J. Wohlgemuth, Jinhong Luo, and Cynthia F. Moss. “Three-dimensional auditory localization in the echolocating bat,” *Current Opinion in Neurobiology *41 (2016): 78-86, accessed February 12, 2017, doi: 10.1016/j.conb.2016.08.002. Donald R. Griffin, Frederic A. Webster, and Charles R. Michael. “The echolocation of flying insects by bats,” Animal Behaviour 8 (1960): 141-154, accessed February 12, 2017, doi: 10.1016/0003-3472(60)90022-1. Rolf Muller, Philip Caspers, Yanqing Fu, and Anupam K. Gupta. “Bioinspired dynamic sensing of acoustic waves,” Proceedings of the ASME/JSME/KSME Joint Fluids Engineering Conference 1 (2015): V001T04A002, accessed February 12, 2017, doi: 10.1115/AJKFluids2015-4680. More From Thats Life [Science]

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Order of Operations Lesson Plans |Addition Math Trail Worksheet||Algebra - Addition Workbook| |Addition Math Crossnumbers||Equation Worksheet Maker| |Algebra Starter Pack||Math Trail Worksheet Maker| |Advanced Algebra Pack||Math Puzzle Maker| - Basic Algebra- In the first lesson, you learned that numbers and variables form sentences, or algebraic "expressions." - Bowling Over the Order of Operations - After learning how to solve equations using the order of operations, students will use their skills to create equations that will "knock down bowling pins". - Domino Math- By making dominoes with different combinations of addition and multiplication problems, students will use a familiar game to learn math skills. Students will build skills in math by matching the answers. - Equivalent or Non-Equivalent - Students will be able to identify and construct equivalent sets. - Everything Balances Out in the End - Students will balance shapes on the pan balance applet to study equality, essential to understanding algebra. Equivalent relationships will be recognized when the pans balance, demonstrating the properties of equality. - Order of Operations - TLWD application of order of operations by solving problems using the correct order of operations. - Order of Operations- To use grouping symbols and the standard order of operations to simplify numerical expressions. - Order of Operations- Using "PEMDAS" - Order of Operations- The students will follow the four-step order of operations procedures. - Order of Operations Bingo - Instead of calling numbers to play Bingo, you call (and write) expressions to be evaluated for the numbers on the Bingo cards. The operations in this lesson are addition, subtraction, multiplication, and division. None of the expressions contain exponents. - Order Of Operations Worksheets - Word Problems- After listening to the story And the Doorbell Rang, students create and solve their own mathematics story problems.

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Introduction to Economics This Introduction to Economics lesson plan also includes: - Join to access all included materials Pupils demonstrate an understanding of the concepts of unlimited wants and limited resources. They participate in an activity using money to purchase goods and services. Students evaluate benefits and costs resulting from personal choices. 3 Views 1 Download - Activities & Projects - Graphics & Images - Handouts & References - Lab Resources - Learning Games - Lesson Plans - Primary Sources - Printables & Templates - Professional Documents - Study Guides - Graphic Organizers - Writing Prompts - Constructed Response Items - AP Test Preps - Lesson Planet Articles - Interactive Whiteboards - All Resource Types - Show All See similar resources: Financial Fables: Shopping Wisely with Olivia Owl Cover two subjects with one lesson! First, dive into English language arts; read an eBook, answer comprehension questions, and complete a cause and effect chart about the financial fable, Shopping Wisely with Olivia Owl. Then, take a... K - 5th Math CCSS: Adaptable Idea Book – For Creating Lessons and Units About American Indians Augment a unit on the traditions and legacies of Native Americans with an informational packet. With pages that detail the tribal origins of commonly used words, a list of ways that Native American customs influenced American democracy,... 2nd - 8th Social Studies & History CCSS: Adaptable Elementary Economics:Making Smart Choices Students understand what good and bad choices are in regards to money and review and reinforce the value of each coin. They identify parts of a story as well as the sequencing. They then create their own sequence of events in words... 1st - 2nd Social Studies & History Reality Store: How to Plan a Budget, Pay Bills, and Manage Your Money Students plan a budget and pay bills when they visit the "Reality Store," a series of classroom studying stations. The use of paying bills and running a class store is used to help students grasp the concept of business. 1st - 5th Social Studies & History

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Angle Properties, Postulates, and Theorems In order to study geometry in a logical way, it will be important to understand key mathematical properties and to know how to apply useful postulates and theorems. A postulate is a proposition that has not been proven true, but is considered to be true on the basis for mathematical reasoning. Theorems, on the other hand, are statements that have been proven to be true with the use of other theorems or statements. While some postulates and theorems have been introduced in the previous sections, others are new to our study of geometry. We will apply these properties, postulates, and theorems to help drive our mathematical proofs in a very logical, reason-based way. Before we begin, we must introduce the concept of congruency. Angles are congruent if their measures, in degrees, are equal. Note: "congruent" does not mean "equal." While they seem quite similar, congruent angles do not have to point in the same direction. The only way to get equal angles is by piling two angles of equal measure on top of each other. We will utilize the following properties to help us reason through several geometric proofs. A quantity is equal to itself. If A = B, then B = A. If A = B and B = C, then A = C. Addition Property of Equality If A = B, then A + C = B + C. Angle Addition Postulate If a point lies on the interior of an angle, that angle is the sum of two smaller angles with legs that go through the given point. Consider the figure below in which point T lies on the interior of ?QRS. By this postulate, we have that ?QRS = ?QRT + ?TRS. We have actually applied this postulate when we practiced finding the complements and supplements of angles in the previous section. Corresponding Angles Postulate If a transversal intersects two parallel lines, the pairs of corresponding angles are congruent. Converse also true: If a transversal intersects two lines and the corresponding angles are congruent, then the lines are parallel. The figure above yields four pairs of corresponding angles. Given a line and a point not on that line, there exists a unique line through the point parallel to the given line. The parallel postulate is what sets Euclidean geometry apart from non-Euclidean geometry. There are an infinite number of lines that pass through point E, but only the red line runs parallel to line CD. Any other line through E will eventually intersect line CD. Alternate Exterior Angles Theorem If a transversal intersects two parallel lines, then the alternate exterior angles are congruent. Converse also true: If a transversal intersects two lines and the alternate exterior angles are congruent, then the lines are parallel. The alternate exterior angles have the same degree measures because the lines are parallel to each other. Alternate Interior Angles Theorem If a transversal intersects two parallel lines, then the alternate interior angles are congruent. Converse also true: If a transversal intersects two lines and the alternate interior angles are congruent, then the lines are parallel. The alternate interior angles have the same degree measures because the lines are parallel to each other. Congruent Complements Theorem If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent. Congruent Supplements Theorem If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent. Right Angles Theorem All right angles are congruent. Same-Side Interior Angles Theorem If a transversal intersects two parallel lines, then the interior angles on the same side of the transversal are supplementary. Converse also true: If a transversal intersects two lines and the interior angles on the same side of the transversal are supplementary, then the lines are parallel. The sum of the degree measures of the same-side interior angles is 180°. Vertical Angles Theorem If two angles are vertical angles, then they have equal measures. The vertical angles have equal degree measures. There are two pairs of vertical angles. (1) Given: m?DGH = 131 First, we must rely on the information we are given to begin our proof. In this exercise, we note that the measure of ?DGH is 131°. From the illustration provided, we also see that lines DJ and EK are parallel to each other. Therefore, we can utilize some of the angle theorems above in order to find the measure of ?GHK. We realize that there exists a relationship between ?DGH and ?EHI: they are corresponding angles. Thus, we can utilize the Corresponding Angles Postulate to determine that ?DGH??EHI. Directly opposite from ?EHI is ?GHK. Since they are vertical angles, we can use the Vertical Angles Theorem, to see that ?EHI??GHK. Now, by transitivity, we have that ?DGH??GHK. Congruent angles have equal degree measures, so the measure of ?DGH is equal to the measure of ?GHK. Finally, we use substitution to conclude that the measure of ?GHK is 131°. This argument is organized in two-column proof form below. (2) Given: m?1 = m?3 Prove: m?PTR = m?STQ We begin our proof with the fact that the measures of ?1 and ?3 are equal. In our second step, we use the Reflexive Property to show that ?2 is equal to itself. Though trivial, the previous step was necessary because it set us up to use the Addition Property of Equality by showing that adding the measure of ?2 to two equal angles preserves equality. Then, by the Angle Addition Postulate we see that ?PTR is the sum of ?1 and ?2, whereas ?STQ is the sum of ?3 and ?2. Ultimately, through substitution, it is clear that the measures of ?PTR and ?STQ are equal. The two-column proof for this exercise is shown below. (3) Given: m?DCJ = 71, m?GFJ = 46 Prove: m?AJH = 117 We are given the measure of ?DCJ and ?GFJ to begin the exercise. Also, notice that the three lines that run horizontally in the illustration are parallel to each other. The diagram also shows us that the final steps of our proof may require us to add up the two angles that compose ?AJH. We find that there exists a relationship between ?DCJ and ?AJI: they are alternate interior angles. Thus, we can use the Alternate Interior Angles Theorem to claim that they are congruent to each other. By the definition of congruence, their angles have the same measures, so they are equal. Now, we substitute the measure of ?DCJ with 71 since we were given that quantity. This tells us that ?AJI is also 71°. Since ?GFJ and ?HJI are also alternate interior angles, we claim congruence between them by the Alternate Interior Angles Theorem. The definition of congruent angles once again proves that the angles have equal measures. Since we knew the measure of ?GFJ, we just substitute to show that 46 is the degree measure of ?HJI. As predicted above, we can use the Angle Addition Postulate to get the sum of ?AJI and ?HJI since they compose ?AJH. Ultimately, we see that the sum of these two angles gives us 117°. The two-column proof for this exercise is shown below. (4) Given: m?1 = 4x + 9, m?2 = 7(x + 4) In this exercise, we are not given specific degree measures for the angles shown. Rather, we must use some algebra to help us determine the measure of ?3. As always, we begin with the information given in the problem. In this case, we are given equations for the measures of ?1 and ?2. Also, we note that there exists two pairs of parallel lines in the diagram. By the Same-Side Interior Angles Theorem, we know that that sum of ?1 and ?2 is 180 because they are supplementary. After substituting these angles by the measures given to us and simplifying, we have 11x + 37 = 180. In order to solve for x, we first subtract both sides of the equation by 37, and then divide both sides by 11. Once we have determined that the value of x is 13, we plug it back in to the equation for the measure of ?2 with the intention of eventually using the Corresponding Angles Postulate. Plugging 13 in for x gives us a measure of 119 for ?2. Finally, we conclude that ?3 must have this degree measure as well since ?2 and ?3 are congruent. The two-column proof that shows this argument is shown below.

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Giving students effective feedback and helping them to "explain their thinking" will let you determine their depth of understanding. It will also give you a chance to clear up any misconceptions before moving on to more difficult concepts. Excel Math lessons have discussion questions and teaching tips built into the Teacher Edition for Kindergarten through Grade Six. Create A Problem Exercises begin with Grade 2 and provide a template for students to write and solve their own word problems, merging math with literacy. In Excel Math we suggest the teacher help students verbalize the problem-solving strategies they use as they solve problems. |Create A Problem from Excel Math lesson sheets for Grade 3| Describing the process can help their classmates understand that at times there can be several correct ways to solve one problem. Remind your students to show their work as they solve the problem so if they have errors in the solution, they can find and fix them more easily. Explain that making mistakes and correcting them is the way to improve and learn. Excel Math includes a unique CheckAnswer system beginning in Grade 2 that lets students check their own work. Most of the time, students can find and correct their mistakes on their own. When they need more help, a parent or teacher can help them work through the problem to find the correct answer. Here are three steps to giving students effective feedback: 1. Ask if they understand the question or problem: a. What information are they trying to obtain? Have them circle the question.2. If there is not enough information, ask the student to tell you what information they would need to answer the question or solve the problem. b. What information have they been given? Have them draw a line under the information that will be needed and cross out the information that will not be needed. c. Do they have the information that they need to get the answer? Find out if the information they have is enough to answer the question. 3. If there is enough information, ask the student to tell you if they underlined the correct information that will be needed. Did they underline too much or little information to solve the problem? If so, have them fix it. After following these three steps with your students, try using questions and statements rather giving answers when someone is having trouble remembering what to do to solve a math problem. You could ask: What do you think you need to do first to find the answer? Do you understand what the question is asking? Tell me in your own words. (This is a good place to make sure any vocabulary words used in the problem are clearly defined and understood.)Take a look at the strategies you use to give your students feedback. What steps should you take to find the solution? Show me how you figured that out. Tell me about the problem-solving strategy you used. What other ways could you have solved this problem? Do any of them need to be modified? Could you use the buddy system to have students help each other find the solutions? Share your suggestions in the Comments box below. New to Excel Math? Preview elementary math lessons that really work for Kindergarten through Sixth Grade on our website: www.excelmath.com. Also find math resources for teachers, parents and students and download a sample packet at excelmath.com.

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The purpose of this activity is to learn to use numbers, an important step toward learning how to add and subtract.From the Virtual Pre-K: Ready For Math toolkit Cut out 20 playing-card sized rectangles from the empty cereal box. Make two sets of cards from 1 to 10. You can make dots to represent each number (one dot for 1, two dots for 2), and add the written numbers as your child starts recognizing numerals. You can also make cards with the written number on one side and the number of dots on the other. Number Card Game Ideas: Which is More?: Help your child count out 10 cards for each of you. Each player puts down one card, then together read the two numbers and decide which is more. The player with the larger number wins both cards. Continue playing until one player has all the cards.

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Red shift. Illustration of galaxies distributed in Space, with the furthest galaxies red due to red shift. This effect was discovered by amateur astronomer William Huggins in 1868, who noticed that the light from some stars was further towards the red end of the spectrum. Huggins realised this was due to the Doppler effect: just as the noise of a moving vehicle changes as it passes, so light from a star changes in wavelength as the star moves towards or away from us. Stars moving away more quickly are more red. In 1929 another astronomer, Edwin Hubble, used red shift to show that the fastest receding galaxies are also the most distant, indicating that the Universe is expanding. Model release not required. Property release not required.

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Topic B begins with the definition of similarity and the properties of similarities. In Lesson 8, students learn that similarities map lines to lines, change the length of segments by factor r, and are degree-preserving. In Lesson 9, additional properties about similarity are investigated; first, students learn that congruence implies similarity (e.g., congruent figures are also similar). Next, students learn that similarity is symmetric (e.g., if figure A is similar to figure B, then figure B is similar to figure A) and transitive (e.g., if figure A is similar to figure B, and figure B is similar to figure C, then figure A is similar to figure C.) Finally, students learn about similarity with respect to triangles. Lesson 10 provides students with an informal proof of the angle-angle criterion for similarity of triangles. Lesson 10 also provides opportunities for students to use the AA criterion to determine if a pair of triangles is similar. In Lesson 11, students use what they know about similar triangles and dilation to find an unknown side length of one triangle. Since students know that similar triangles have side lengths that are equal in ratio (specifically equal to the scale factor), students verify whether or not a pair of triangles is similar by comparing their corresponding side lengths. In Lesson 12, students apply their knowledge of similar triangles and dilation to real world situations. For example, students use the height of a person and the height of his shadow to determine the height of a tree. Students may also use their knowledge to determine the distance across a lake, the height of a building, and the height of a flagpole.

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I have the students gather in a circle on the carpet. I give them each analog clock I will use the white board to write down digital times. "I will write a time on the board using digital notation. Your job will be to set your clock to match that time. when you are finished, you should hold up your clock so that I can see your answer." I repeat this with hour and half hour times. At this point in the year, I am reviewing established routines and concepts from the year long curriculum. This activity is meant for students who are familiar with the use of a clock and understand the basic time concepts. I also like using this warm up for a fraction lesson because of the connection between clocks and fractions (half past, quarter past, etc.). This activity has students telling and writing times to hours and half hours (CCSS.MATH.CONTENT.1.MD.B.3). Advanced Preparation: You will need to create two posters (Squares Poster and Circles Poster) before the lesson starts. You will notice that I lightly drew in the lines for quartering each shape. This way I could make sure they were precise, and it also saves time as you start the lesson. I start with the circle poster. "We have been talking about halves. What happens if I divide a circle in half (draw a line through the middle of the first circle)? What can you tell me about the two pieces? What if I draw another line and create 4 equal pieces? Does anyone know what that is called? You're correct, Fourths or Quarters. When you break something into fourths, it not only has 4 pieces but each piece has to be equal." The rest of your conversation should focus on the fact that fourths means 4 equal pieces, that a fourth is one part of the whole, and 4 fourths make 1 whole. I then move onto the second circle and use a market to define the lines dividing the circle into four unequal parts. "Is this broken into fourths?" I had included a video (Quartering Circles.m4v) with a student's explanation of why it is not. I then use the squares poster and repeat the above procedure. I have also included a photo of the Completed Squares Poster (after the discussion). You will see that we crossed out ones that were not fourths as we went. This activity has students partitioning shapes into four equal shares, describe the shares using the words fourths,and the phrase quarter of. They are also asked to describe the whole as four of the shares (CCSS.MATH.CONTENT.1.G.A.3). Advanced Preparation: You will need to make enough copies of Square Cakes for your class. You wil also need rulers, markers, crayons, and scissors. Please watch the video, Introducing Quarter Cakes to see how to introduce this activity to your class. "I want you to now go find a spot int he room to work on your own cakes. Remember to color each half a different color." I have included a photo, Creating Cakes, of a student working on her cakes. To end today's lesson, I will ask that students complete the exit ticket, Finding Fourths. I will work with students that I saw struggling with the concept during the Quarter Cakes activity. I will ask the students to meet me on the carpet and hand out their sheet for today's Mad Minute exercise. This routine was introduced in a previous lesson. Please check out the link to get a full overview of this routine. I want to really focus on fact fluency and build upon the students ability to solve within ten fluently (CCSS.MATH.CONTENT.1.OA.C.6). I am going to use the Mad Minute Routine. This is a very "old school" routine, but I truly feel students need practice in performing task for fluency in a timed fashion. Students need to obtain fact fluency in order to have success with multiplicative reasoning. Students who don't gain this addition fact fluency by the end of 2nd grade tend to struggle with the multiplicative reasoning in third. Having this fluency also allows them to work on more complex tasks because the have the fact recall to focus on the higher level concepts.

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The word Geometry has been derived from the Greek word “Geometron” “Geo” means Earth and “Metron” means measurement . Three geometrical terms namely Point, Line and Plan form the foundation of Geometry. Through the chapters covered in this section ( Basic Concepts, Angles, Triangles, Symmetry, Construction) students will be able to build a strong foundation in this area. We provide theory, MCQs and assignments for each individual topic. Click on each topic to know more details. - Properties of different quadrilaterals-square, rectangles, rhombus, trapezium and parallelograms - Parallel lines and transversals Students will be introduced to the fundamental concepts of geometry – point, line and plane. We will cover different types of quadrilaterals – Parallelogram, Rectangle, Square, Rhombus, Trapezium kites etc and discuss their properties in detail. Read more about this course. - Finding different types of angles –Acute, Obtuse, right angles - Supplementary and Complementary angles - Vertically Opposite angles In this chapter, we will discuss the concept of an angles, cover different types of angles and their properties. Read more about this course.

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Students will read a graph correctly and use the graph to find information. Common Core Standard Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Puppy Growth article Click Here - Have students read this article about the way puppies grow. Click Here - Review the attributes of a graph, including x-axis and y-axis. Explicit Instruction/Teacher Modeling - Display sample graph below. Ask students the following questions: - What does the x-axis represent? - What does the y-axis represent? - How many facts did I get correct on day 2? Independent Working Time - Have students complete the puppy growth questions independently. Review and Closing - Review the correct answers with the class. Burke, A. (2016, August 22). When Does My Puppy Finish Growing? Retrieved fromhttps://www.akc.org/content/dog-care/articles/when-does-my-puppy-finish-growing/

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In Plate Tectonic Theory, the lithosphere is broken into tectonic plates, which undergo some large scale motions. The boundary regions between plates are aptly called plate boundaries. Based upon their motions with respect to one another, these plate boundaries are of three kinds: divergent, convergent, and transform. Divergent boundaries are those that move away from one another. When they separate, they form what is known as a rift. As the gap between the two plates widen, the underlying layer may be soft enough for molten lava underneath to push its way upward. This upward push results in the formation of volcanic islands. Molten lava that succeeds in breaking free eventually cools and forms part of the ocean floor. Some formations due to divergent plate boundaries are the Mid-Atlantic Ridge and the Gakkel Ridge. On land, you have Lake Baikal in Siberia and Lake Tanganyika in East Africa. Convergent boundaries are those that move towards one another. When they collide, subduction usually takes place. That is, the denser plate gets subducted or goes underneath the less dense one. Sometimes, the plate boundaries also experience buckling. Convergent boundaries are responsible for producing the deepest and tallest structures on Earth. Among those that have formed due to convergent plate boundaries are K2 and Mount Everest, the tallest peaks in the world. They formed when the Indian plate got subducted underneath the Eurasian plate. Another extreme formation due to the convergent boundary is the Mariana Trench, the deepest region on Earth. Transform boundaries are those that slide alongside one another. Lest you imagine a slippery, sliding motion, take note that the surfaces involved are exposed to huge amounts of stress and strain and are momentarily held in place. As a result, when the two plates finally succeed in moving with respect to one another, huge amounts of energy are released. This causes earthquakes. The San Andreas fault in North America is perhaps the most popular transform boundary. Transform boundary is also known as transform fault or conservative plate boundary. Movements of the plates are usually just a few centimeters per year. However, due to the huge masses and forces involved, they typically result in earthquakes and volcanic eruptions. If the interactions between plate boundaries involve only a few centimeters per year, you could just imagine the great expanse of time it had to take before the land formations we see today came into being. You can read more about plate boundaries here in Universe Today. Here are the links: - Tectonic Plates Here are the links of two more articles from USGS: Here are two episodes at Astronomy Cast that you might want to check out as well:

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Plants play a big role in removing carbon from the atmosphere. Almost a quarter of carbon from car exhaust and industry gets absorbed by vegetation. That’s a significant amount. But a recent study suggests that amount has the potential to be much larger. A team of European researchers pulled together myriad data sources to create a series of maps that suggest the earth’s potential vegetation biomass—that is, just how much greenery our planet could support and where, were it not for the impact of humankind. In principle, a landscape untouched by humans is at its full potential whether a rich rainforest or desert; a forest thinned by logging, for example, has less than its potential vegetation biomass—a clear-cut forest has even less. While deforestation is a well-known cause of vegetation loss, the team’s findings, published in Nature, show that widespread land management practices such as logging or grazing-depleted grassland create nearly as large a gap between potential and actual amounts of vegetation on the global scale. Estimating global vegetation biomass has proven challenging. Some researchers use the heights and diameters of a series of trees to estimate the biomass of a forest—a time-intensive approach that provides good estimates for an individual forest but is difficult to translate to larger areas. Others rely on satellite sensing technologies that capture sweeping swaths of green but provide coarser estimates. A coffee plantation with shade trees looks much like a forest from space, notes environmental physicist Sassan Saatchi of NASA’s Jet Propulsion Laboratory. Land systems scientist and lead author Karl-Heinz Erb of Alpen-Adria University in Austria and colleagues took a different approach. “What are the best maps out there from different schools of thinking?” he questioned. “Let’s put them together and analyze how robust the signal of human impact is.” The researchers identified over ten previously published datasets, including data from Saatchi, who was not involved in the study. Dataset sources included land-use data, on-the-ground plant censuses, and remote satellite sensing. The team then created six global maps of vegetation biomass by drawing on different combinations of datasets. They borrowed a seventh map from the literature. By averaging the total amounts of vegetation suggested by each map, the team estimated that the earth’s vegetation stores about 450 petagrams of carbon. (Humans currently release about 9 petagrams of carbon into the atmosphere each year.) The team then created five maps estimating the potential global vegetation biomass by drawing on additional datasets. These included remote sensing data that could identify remnants of natural vegetation and ecological databases of the typical carbon contents of different vegetation types. The team also used an existing map, which estimates the carbon stock lost when converting natural vegetation to cropland across the globe. By taking the median of the differences between each of 42 possible pairs from the two sets of maps, the team found that, were it not for humans, the earth could double its vegetation. Their findings also suggest that land cover change, such as converting a forest to farmland, is responsible for over 50 percent of the difference between actual and potential vegetation. Meanwhile, land management, such as thinning a forest through logging or grazing, is nearly as damaging, accounting for 42-47% of the difference. This quantification of the impact of land management is a really important advance, says environmental scientist Edward Mitchard of the University of Edinburgh, who was not involved in the study. “There is a lot of talk in the news media about deforestation,” he says. “But forest degradation, where you take out some trees, probably affects an area that is between 2 and 10 times larger every year.” “This paper could help policymakers to really pay attention to that level of degradation and to design techniques to monitor,” says Saatchi. Indeed, the United Nations’ REDD+ program, includes limiting forest degradation among its carbon emission reduction goals. Saatchi does wonder, however, whether the paper’s potential vegetation biomass figure may be an overestimate, possibly biased by researchers favoring sampling “beautiful majestic forests” over naturally sparse ones. If vegetation could reach the global potential estimated here, it could store the equivalent of 50 years of carbon emissions. This, of course, is an impossible goal. “We are 7.5 billion people,” says Erb. “We need cropland to feed ourselves, forests to build houses.” Still, by identifying the large impact of land management practices, Erb believes his study suggests that encouraging vegetation for increased carbon absorption is an option. “There is quite a potential for refilling the forests,” he says.

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Beacon Lesson Plan Library Teacher, We Shrunk the Classroom DescriptionThe students will use the metric system or standard measurement to measure the perimeter of the classroom; area of the floor, walls, chalkboard, teacher desk, student desks, closets, etc. to create a scale model of the classroom. ObjectivesThe student solves real-world problems involving perimeter, area, capacity, and volume using concrete, graphic or pictorial models. -Cardboard and/or Cereal boxes -"RESULTS" Worksheet (attached file) 1. Make sure you have cardboard, cereal boxes, construction paper, scissors, tape, rulers, yard sticks, etc. 2. Have groups chosen ahead of time. 3. Make up a "Results" recording sheet with clear directions (See attached file.) 4. Measure the class items ahead of time to verify the accuracy of the students' measurements. 1. Review the measurement system you will use (metric/standard) as well as perimeter, area, height, width, length, ratio, and scale model. 2. Students work with a partner or group to measure a particular part of the classroom that the teacher assigns to them. (Examples: door, teacher desk, student desk, chalkboard, closet, floor, windows.) 3. Measurements for length, width, height, perimeter, and area are recorded on a "RESULTS" worksheet. All measurements should be double checked for accuracy. Students peer check each other's measurements. The teacher should check all measurements as well. 4. Convert the measurements to 10:1 size on their paper of results.Discuss how to create a scale model. Check all measurements for accuracy. 5. Each pair or group is given the materials to create a scale model of the object they measured out of cardboard, construction paper, etc. 6. Each pair or group adds their model to the scale model to create a replica of the classroom that is 1/10 the size of the actual room. 7. Students write a summary of the sequential steps taken to create the model and read the summary to the class. Students will fill out a "Results" sheet with the actual measurements they have made for each item; including perimeter, height, width, length, and area. The teacher will check these for accuracy. Then each student will compute a 10:1 ratio for each measurement. Students can peer check one another. Then one student from each group can bring the results to the teacher to be checked. When all measurements are correct, students will make a scale model of their item (table, desk, wall) that is 1/10 the size of the actual item. The teacher will measure these scale models to ensure the students have achieved the desired objective of the lesson. Students will then peer check the scale models of their classmates. The students should be able to accurately measure quantities in the real world and use the measures to solve problems. If students do not have accurate measurements, additional practice will need to be given. A student has mastered the standard being evaluated if he/she uses the correct measurements on the item, calculates the correct scale model ratio numbers, and produces a 3 dimensional scale model based on the perimeter and area measurements taken at the beginning of the lesson. Attached FilesStudent "Results" worksheet to record measurements. File Extension: pdf Return to the Beacon Lesson Plan Library.

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Beacon Lesson Plan Library Point of You DescriptionStudents learn about point of view by rewriting an existing narrative paragraph (using a different point-of-view). Students expand this knowledge by writing an expository paragraph, then rewriting it to reflect a different point-of-view. ObjectivesThe student discusses the meaning and role of point of view in a variety of texts. The student selects and uses a format for writing which addresses the audience, purpose, and occasion (including but not limited to narrative, persuasive, expository). The student understands the role of point of view in a literary or informational text. The student knows the point of view of a literary work and how it affects the story line. Materials--Narrative Paragraph (teacher-created or any other source) --Chalk/Dry Erase Board OR Overhead Projector --Chalk, Dry-Erase Markers, OR Overhead Pens --'Point of You' Questions/Assessment (one copy for each student) Preparations1. Create a narrative paragraph that describes a considerable amount of action so students will be able to see the differences in point of view more easily. In lieu of creating a paragraph, you may use a paragraph from any text that is not copyrighted. 2. Create a transparency of the paragraph you will use, or copy the paragraph on the board. 3. Download and copy the 'Point of You' assessment sheet (attached file) for each student. a. Write 'Point of You' on the board/overhead to gain students' attention and find out if anyone recognizes your play on words. Change it to 'Point of View'. Ask students to think about a time when they tried to get their parents to allow them to do something they really wanted to do, but their parents wouldn't let them do it, making it seem as though their parents just didn't understand their 'side' of things. b. Dramatize a personal experience for the students to show how the role of point of view plays an important part in our ability to understand a situation, or even what we read. (I like to relate an experience about a time during middle school when I was not allowed to wear the clothes of 'my' choice. I felt as though my parents didn't understand why I wanted to wear them, and I certainly didn't understand why they didn't want me to wear them. Our differing points of view led to more than one misunderstanding during those middle-school years.) First, enter the room as your teenage self and describe, in teenage terminology, the time your parents wouldn't let you wear some particular piece of clothing (Use a lot of emotion, OR just keep your arms crossed the entire time). Then, leave the room and reenter as one of your parents. This time you'll relate what happened in a very calm way, using more 'logical' reasoning for your decision about the clothing. Leave the room one final time and reenter as yourself (Thank goodness!). c. Explain that point of view is the way people see/experience things differently than others do. Discuss how being aware of different points of view can enable them to understand other people's thoughts/reactions related to experiences, as well help them have a better understanding of what they read. d. Display the narrative paragraph on the board/overhead. e. Call on students to identify the person who is telling the story. Is it first person (told from the view of a character in the story), or is it third person (told from the view of someone other than a character in the story)? f. Discuss how a first-person point of view can be the best way to tell a story. Discuss how a third-person point of view can be the best way to tell a story. g. Show how the story line would be different if told from another point of view. With the students' help, rewrite the paragraph using a different point of view. Draw attention to the way both paragraphs tell the same story with regard to what happened, but how the rewrite enabled them to see the events in a different way, which is another point of view. h. Have students write an expository paragraph that describes an object (CD, make-up, skateboard, pencil, etc.) and how the object is used. i. Have students to imagine their objects as having the ability to speak. Ask them to rewrite their paragraphs from the object's point of view, making sure to include all of the facts given in the first paragraph. Remind students that the objects might want to add some information about how they feel. Circulate to assist students who might need a sentence or two to get them started. g. Call on volunteers to share both of their paragraphs. h. Distribute the 'Point of You' sheet. Have students respond to the questions, and staple them behind their paragraphs before you collect them. i. Complete the 'Point of You' sheet to determine each student's achievement of the selected SSS. AssessmentsUse the 'Point of You' sheet (file available in this lesson), attached to students' work, to assess students' achievement of the selected SSS. A combined score may be earned on all three pieces (para.1 @25 points, para.2 @25 points, and the 'Point of You' questions/responses @ 50 points--10 pts. per item). Attached FilesThe 'Point of You' sheet is used to allow students to respond to questions related to SSS, and to allow the teacher to assess achievement of the SSS. File Extension: pdf Return to the Beacon Lesson Plan Library.

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Sine (sin) function - Trigonometry of the triangle and see how the sine of A and C are calculated. The sine function, along with cosine and tangent, is one of the three most common In any right triangle, the sine of an angle x is the length of the opposite side (O) divided by the length of the In a formula, it is written as 'sin' without the 'e': Often remembered as "SOH" - meaning See SOH CAH TOA As an example, let's say we want to find the sine of angle C in the figure above (click 'reset' first). From the formula above we know that the sine of an angle is the opposite side divided by the hyupotenuse. The opposite side is AB and has a length of 15. The hypotenuse is AC with a length of 30. So we can write which comes out to 0.5. So we can say "The sine of 30° is 0.5 ", or Use your calculator to find the sine of 30°. It should come out to 0.5 as above. (If it doesn't - make sure the calculator is set to work in degrees and not Example - using sine to find the hypotenuse If we look at the general definition - we see that there are three variables: the measure of the angle x, and the lengths of the two sides (Opposite and Hypotenuse). So if we have any two of them, we can find the third. In the figure above, click 'reset'. Imagine we didn't know the length of the hypotenuse H. We know that the sine of A (60°) is the opposite side (26) divided by H. From our calculator we find that sin60 is 0.866, so we can write which comes out to 30.02 * The lengths and angles in the figure above are rounded for clarity. Using a calculator, they will be slightly different. The calculator is correct. The inverse sine function - arcsin For every trigonometry function such as sin, there is an inverse function that works in reverse. These inverse functions have the same name but with 'arc' in front. (On some calculators the arcsin button may be labelled asin, or sometimes So the inverse of sin is arcsin etc. When we see "arcsin A", we understand it as "the angle whose sin is A" Use it when you know the sine of an angle and want to know the actual angle. |sin30 = 0.5 ||Means: The sine of 30 degrees is 0.5 |arcsin0.5 = 30 ||Means: The angle whose sin is 0.5 is 30 degrees. See also Arc sine definition and Inverse functions - trigonometry Large and negative angles In a right triangle, the two variable angles are always less than 90° (See Interior angles of a triangle). But we can find the sine of any angle, no matter how large, and also the sine of negative angles. For more on this see Functions of large and negative angles. Graphing the sine function When the sine of an angle is graphed against the angle, the result is a shape similar to that on the right, called a sine wave. For more on this see Graphing the sine function. The derivative of sin(x) In calculus, the derivative of sin(x) is cos(x). This means that at any value of x, the rate of change or slope of sin(x) is cos(x). For more on this see Derivatives of trigonometric functions together with the derivatives of other trig functions. See also the Calculus Table of Contents. While you are here.. ... I have a small favor to ask. Over the years we have used advertising to support the site so it can remain free for everyone. However, advertising revenue is falling and I have always hated the ads. So, would you go to Patreon and become a patron of the site? When we reach the goal I will remove all advertising from the site. It only takes a minute and any amount would be greatly appreciated. Thank you for considering it! – John Page Become a patron of the site at patreon.com/mathopenref Other trigonometry topics Solving trigonometry problems (C) 2011 Copyright Math Open Reference. All rights reserved

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Lesson Plan – Musical Moods Music appreciation and interpretation through visual art – Allows students to respond to music from different cultures through abstract line drawing. - To enhance students’ awareness of the presence of music in all cultures. - To aid students’ appreciation of the variety of sounds in music. - To develop students’ understanding of the moods conveyed by music. - To represent musical qualities through visual art. - Three short pieces of music, each from a different culture and with contrasting qualities/moods. - Large coloured crayons. - Sheets of A3 paper – one per piece of music, per student. - Edicol or food dyes in a variety of colours. What to do - Teacher facilitates a whole class discussion about the students’ favourite music, why they like it and how it makes them feel. - Students listen to the three pieces of music. - After listening to each piece again, students offer words or phrases to describe the music: these may refer to the sounds, mood or instruments being played. - Students are asked to speculate about a situation in which each piece of music would be suitable eg for dancing, as a lullaby, for an action film etc. - Students listen to the first piece again and this time depict the music through a line drawing. Students choose a coloured crayon which they feel ‘matches’ the piece and may be guided by the following instructions: ‘Start with your crayon in a corner of your paper. While you are listening to the music, draw how the music sounds to you by letting your crayon wander across and around the paper. Feel the music in your hand. Make shapes with your line drawing that look like the music feels.’ It may be helpful to model this process for students using one of the pieces of music. - Students compare their line drawings and teacher elicits descriptions of similarities and differences between them. Teacher tells students about the cultural origin and use (if applicable) of the piece of music. - Repeat steps 5 and 6 for the other two pieces of music, using a separate piece of paper and a different coloured crayon for each one. - Students apply a coloured wash over each drawing, choosing a colour and style they feel is appropriate. - The pictures may be grouped together for each piece of music for display. Students may use other means of interpreting the music, including: - facial expressions - hand movements - dance movements. Adapted from a Living in Harmony Funded Project, ‘All Together Now’, Churches’ Commission on Education, WA, 1999.

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Many factors affect rates of chemical reactions - pressure of gases, temperature, surface area of solids, concentration and if there is a catalyst. Anything that will change the probability of particles colliding or change the energy of the collisions will affect the rate of a reaction. This is the first of three GCSE Chemistry quizzes looking at these factors. The rate of a reaction is a measure of how quickly a chemical reaction progresses. Some reactions can be very slow, for example rusting can take weeks or even years, whilst others, such as neutralisation or an explosion are over very rapidly. The rate of reaction is very important in industrial situations; take explosions for instance - these are incredibly fast reactions. An explosive is a solid that turns into a huge amount of very hot gas VERY quickly! This makes them useful for several purposes - most notably in warfare - though a more peaceful use is in the quarrying for resources. At a quarry, they drill holes with a diameter of a few centimetres down into the rocks. They then drop sticks of explosives into the holes along with a detonator. The space above the explosives is then filled with something like sand or fine gravel. When the explosive is ignited (this is an increase in energy, one of the factors which affects the rate of a reaction), it vapourises in a fraction of a second, turning into a huge quantity of gas. The hole that was drilled is far too narrow for the gas to escape quickly. The trapped gas creates a huge pressure since it is confined in such a small volume and this pressure is enough to fracture the rocks, sending them flying into the air. You may have seen video footage of the effect of this fast reaction during your chemistry lessons. Before explosives, quarrying was a much slower and less spectacular process since the quarry workers used hammers and wedges to split the rocks apart. Where there were no natural cracks, they had to make their own holes by hand before they could drive the wedges into the rocks. There are many different ways that you can follow the rate of reaction, you will have used some of them and seen others demonstrated during your GCSE studies. It all comes down to finding ways of measuring how fast the reactants are used up or how quickly the products are made. If one of the products is a gas that can safely be released into the air, life is easy! You can simply let it escape from the reaction vessel and measure how the mass decreases as the reaction proceeds. A better method is to collect the gas and measure how much is produced every few seconds. In a reaction between liquids, if an opaque precipitate or suspension is produced, less and less light will be transmitted through the liquids as the reaction progresses. You could stand the reaction vessel on a piece of paper with a cross on it and time how long it takes for the cross to be obscured. For a more technical solution, use data logging and a light sensor to measure how much light is transmitted through the mixture over the course of the reaction. When measuring the rate of a reaction, what you can't do is just measure a factor at the start or at the end. This does not work, you need to measure something continuously during the reaction, in other words, your measurements must include time. It is best to start timing at the moment that the reactants are mixed and to continue measuring for as much of the reaction as possible. You will then be able to collect sufficient data for it to be both reliable and valid, from which you can plot one or more graphs to help you to draw your conclusions. Have a go at this quiz and see how well you understand how to measure the rates of chemical reactions and the factors which will affect them.

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Students in elementary and middle school learn to use past, present and future tense verbs for speaking, reading and writing purposes. Learning tenses can be challenging for students. However, teachers can enhance the experience of learning verb tenses with hands-on, interactive and fun activities. Teach students to identify and use action verbs in sentences and reading selections. Provide students with hands-on and interactive activities for learning about verbs. Verbs are action words. While students can benefit from identifying action verbs on worksheet assignments, teaching action verbs is the perfect opportunity to get creative. Create a set of action verb cards. Fold each one in half and put the cards in a basket or bowl. Next, allow students to select a card and act out the verb on the card. Students will be jumping, dancing, singing, snoring and doing just about any other action verb you deem appropriate inside the classroom. You can change up this game by acting out the verb yourself. Students love to see teachers act in ways they do not normally act---especially if it means acting silly. Introduce adverbs that allow students to recognize and use present tense verbs. While "kick" is present tense, we may not always use the verb in that particular form. Often we will say or write "always kicks" or "sometimes kicks." Teach students the adverbs that often accompany present tense verbs. These include words such as: now, currently, usually, frequently, seldom, rarely and never. Teach past tense through reading and writing exercises. Biography, memoir and personal narrative reading selections often include many different kinds of past tense verbs. Read a selection aloud to students and allow them to write down each past tense verb they hear. Make a game of it. Tell the students how many past tense verbs are in the selection and provide incentives for students who can name all of them. Students can also write their own personal narrative about an event or experience in their own lives that happened in the past. As students write rough drafts of their narratives, introduce different ways to create past tense verbs. Through the editing and revising process, direct students to enhance their stories by choosing less common and more interesting verbs. This will give students more practice with past tense. Have students talk about their future plans to introduce and teach future tense. Students use future tense in conversation every day. Before introducing the concept of future tense, talk with students about their plans for the evening or weekend. Discuss the concept of the future and point out the future tense verbs students used in conversation. Expand on this exercise by asking students to set goals for the grading period, school year, or even for their future beyond school. Have students write down their goals in either list or paragraph form. Once the students finish this part of the exercise, ask them to highlight all of the future tense verbs they used. - today image by alwayspp from Fotolia.com

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The electoral college was created as a compromise between those at the Constitutional Convention who wanted the U.S. president elected by popular vote and those who wanted Congress to select the president. Instead, electors corresponding to the number of representatives each state had in Congress would elect the president. Objections to a popular vote mainly concerned the difficulty of transmission of information about the candidates to voters throughout the country, which would lead voters in larger states to prefer local politicians with which they were familiar. Voting by Congress alone would potentially upset the governmental balance of power and lead to corruption and political bargaining. A group called the Committee of Eleven proposed the compromise of the Electoral College. Each state would have a total number of electors corresponding to its two senators and the amount of its members in the House of Representatives, which is based on the state's population. Individual state legislatures would decide on how the electors were chosen, assuaging the fear of many states of a too-powerful federal government. To maintain balance in the various branches of the federal government, members of Congress and government employees were not allowed to be electors. The electors would meet in their home states, further forestalling federal intervention. The Constitutional Convention agreed upon the compromise, and the Electoral College system was written into Article II, Section 1 of the Constitution.

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In 1846, a slave named Dred Scott sued in a Missouri court for his freedom. Scott argued that his service for Dr. Emerson in Illinois, a state wherein slavery was not allowed according to the terms of the Missouri Compromise, qualified him for his freedom. Eventually the case found its way all the way to the Supreme Court of the United States. The composition of the court reflected prevailing attitudes in the US at the time. As a result, the court ruled against Scott 7 to 2. The most important aspect of this case was that blacks were considered property rather than people. Since they were property, they could no petition for rights. Chief Justice Taney wrote in his majority opinion that it was beyond dispute that the signers of the Declaration of Independence in 1776 had not intended to include blacks as citizens of the nation that they set out to establish. As a result of this case, the division between the northern states and southern states widened. The economy of the southern states was built on slavery, and much of their social customs and standards revolved around it. The north was increasingly in the grip of abolitionist sentiments and anti-slavery movements. The Dred Scott vs. Sanford case only deepened the divide between north and south. The decision was the apogee of the push to expand slavery. The US was expanding, and the Missouri Compromise resulted in diminishing political power in the north, due to the fact that many new states would be admitted as slave states. As a result, Democratic Party politicians sought to repeal the Missouri Compromise. Finally, in 1854, they succeeded by passing the Kansas-Nebraska act, which permitted states to decide for themselves south of the 40th parallel. With Dred Scott, the Taney court had de facto endorsed the unfettered expansion of slavery into the territories.

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So far, we’ve seen the trigonometry for right-angled triangles. However, we can also apply the trigonometric rules for non-right angled triangles. Let’s first start by the naming conventions for a non-right angled triangle. Each triangle has three points (written in capital letters) that also identify the angle they represent. The sides of a triangle are named with lower case letters opposite the angle they face. For example the side opposite to angle A is given as ‘a’, and so on. There are two trigonometric rules for non-right angled triangles – sine rule and cosine rule. In this section, we look at the sine rule. Definition of Sine Rule The sine rule states that, in a non-right angled triangle, = = is a constant. Let’s see how the above formula is arrived at. In the triangle ABC, draw a perpendicular to BC, so we get two right angled triangles, ABD and ADC. From ABD, sin B = , hence h = c sin B From ADC, sin C = , hence h = b sin C Using the above 2 equations for h, we get h = c sin B = b sin C. Similarly we can show that = . Hence = = Remember: We use sine rule when we have opposite set of pairs of angles, and the sides are involved. Let us look at some examples of sine rule: Example 1: Find the unknown side x in the triangle ABC. x = 7 x = 6.1557 cm Example 2: Find the unknown angle. = = 0.375 = 22.024° = 22°1′ (to the nearest minute) Summary of Sine Rule - When you have to find unknown sides, use the sine rule formula – = = - When you have to find unknown angles, use the following sine rule formula – = =

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The Heat Index, also known as the apparent temperature, is an accurate measure of how hot it really feels when relative humidity (RH) is added to the actual air temperature. The National Weather Service derived the Heat Index in an effort to alert the public to the dangers of exposure to extended periods of heat, especially when high humidity acts along with the high temperatures to reduce the body's ability to cool itself. One important fact to realize about the Heat Index is that it is computed for temperature readings taken in the shade and for a wind speed of approximately 6 miles per hour. Exposure to full sun can add up to 15 ° F to the Heat Index value! To find the Heat Index from the table, find the air temperature along the left side of the table and the relative humidity along the top. Where the two intersect is the Heat Index. Do you keep records of the Heat Index? If not, how do I calculate it? Because the Heat Index is a calculated value based off of air temperature and humidity, it is not archived with historic weather data. To calculate a specific value for a previous date, you will need to know the air temperature and humidity. This data is not typically available for cooperative observing stations, but is generally available for airports. The equation to calculate the Heat Index is as follows: T = air temperature in degrees Fahrenheit RH = relative humidity The Wind Chill Temperature Index, sometimes also known as the equivalent temperature, is used to describe how cold people and animals feel when they experience heat loss caused by the combined effects of low temperature and wind. When the wind blows across exposed skin, it removes the insulating layer of warm air that lies adjacent to the skin. This in turn drives down the skin temperature and eventually the internal body temperature. The faster the wind blows, the faster the heat is carried away, the greater the heat loss and the colder it feels. A new Wind Chill Temperature Index took effect on November 1, 2001, replacing the original wind chill index that was derived in 1945. The original Wind Chill Index was developed by two Antarctic explorers and was based on research involving the time it took water in a plastic container to freeze. The new Wind Chill Temperature Index includes the latest advances in science, technology and computer modeling. It takes into account a calculated wind speed at average face height based on readings from winds measured at the national standard height of 33 feet. It is based on the exposure of a human face to cold versus a plastic container, incorporates modern heat transfer theory, lowers the calm wind threshold from 4 miles per hour to 3 miles per hour, and has a consistent standard for skin tissue resistance. The new Wind Chill Temperature Index currently assumes no impact from the sun, but it may yet be revised again for solar radiation impacts under various sky conditions (clear, partly sunny, cloudy). For additional information on the new Wind Chill Temperature Index, please see http://www.nws.noaa.gov/om/cold/wind_chill.shtml. To find the Wind Chill Temperature Index from the table below, find the air temperature along the top of the table and the wind speed along the left side. Where the two intersect is the Wind Chill Temperature. Lastly, while exposure to low wind chills can be life threatening to humans and animals, the only effect that wind chill has on an inanimate objects, such as vehicles, is that it shortens the time it takes the object to cool to the actual air temperature. The object cannot be cooled below the actual temperature. Do you keep records of Wind Chill? If not, how do I calculate it? Because the Wind Chill Temperature Index is a calculated value based off of air temperature and wind speed, it is not archived with historic weather data. To calculate a specific Wind Chill Temperature for a previous date, you will need to know the air temperature and wind speed. This data is not typically available for cooperative observing stations, but is generally available for airports. The equation to calculate the Wind Chill Temperature Index is as follows: T = air temperature in degrees Fahrenheit V = wind speed in miles per hour Heating Degree Days (HDD) are used as an index to estimate the amount of energy required for heating during the cool season. When the daily mean temperature falls below 65 degrees Fahrenheit, most buildings require heat to maintain a comfortable interior temperature. By monitoring heating fuel usage and heating degree day accumulation over a period of time, a building's energy consumption per HDD can be calculated and this value used, for example, in fuel consumption monitoring, energy efficiency evaluation or future fuel supply estimates. The daily mean temperature is found by adding together the high and low temperature for the day and dividing by two. When the mean temperature is above 65 ° F, the HDD total is zero. If the mean temperature is below 65 ° F, the HDD amount is the difference between 65 ° F and the mean temperature. For example, if the high temperature for the day was 68 ° F and the low 52 ° F, the mean temperature for the day would be 68 + 52 = 120 / 2 = 60 ° F. The Heating Degree Day total would then be 65 60 = 5 HDD. In equation form: TBASE = Heating Degree Day base temperature, usually 65 TMEAN = mean temperature, Cooling Degree Days (CDD) are used as an index to estimate the amount of energy required for cooling during the warm season. When the temperature rises above 65 ° F, many buildings use air conditioning to maintain a comfortable indoor temperature. By monitoring air conditioner energy usage and cooling degree day accumulation over a period of time, a building's energy consumption per CDD can be calculated and this value used, for example, in energy use monitoring, energy efficiency evaluation or future energy usage estimates. The daily mean temperature is found by adding together the high and low temperature for the day and dividing by two. When the mean temperature is below 65 ° F, the CDD total is zero. If the mean temperature is above 65 ° F, the CDD amount is the difference between the mean temperature and 65. For example, if the high temperature for the day was 92 ° F and the low was 68 ° F, the mean temperature for the day would be 92 + 68 = 160 / 2 = 80 ° F. The Cooling Degree Days would then be 80 - 65 = 15 CDD. In equation form: TBASE = Cooling Degree Day base temperature, usually 65 TMEAN = mean temperature, Growing Degree Days (GDD) are used to estimate the growth and development of plants and insects during the growing season. The basic concept is that development will only occur if the temperature exceeds some minimum development threshold, or base temperature (TBASE). The base temperatures are determined experimentally and are different for each organism. |Reported Base Temperatures for GDD Computations| |40° F||wheat, barley, rye, oats, flaxseed, lettuce, asparagus| |45° F||sunflower, potato| |50° F||sweet corn, corn, sorghum, rice, soybeans, tomato| |44° F||Corn Rootworm| |48° F||Alfalfa Weevil| |50° F||Black Cutworm, European Corn Borer| |52° F||Green Cloverworm| To calculate GDDs, you must first find the mean temperature for the day. The mean temperature is found by adding together the high and low temperature for the day and dividing by two. If the mean temperature is at or below TBASE, then the Growing Degree Day value is zero. If the mean temperature is above TBASE, then the Growing Degree Day amount equals the mean temperature minus TBASE. For example, if the mean temperature was 75° F, then the GDD amount equals 10 for a TBASE of 65° F. You can think of Growing Degree Days as similar to Cooling Degree Days, only the base temperature can be something besides 65° F. In equation form: TBASE = Growing Degree Day base temperature TMEAN = mean temperature, Modified Growing Degree Days are similar to Growing Degree Days with several temperature adjustments. If the high temperature is above 86° F, it is reset to 86° F. If the low is below 50° F, it is reset to 50° F. Once the high/low temperatures have been modified (if needed), the average temperature for the day is computed and compared with a base temperature, which is usually 50° F. Modified Growing Degree Days are typically used to monitor the development of corn, the assumption being that development is limited once the temperature exceeds 86° F or falls below 50° F. For example, if the high for the day was 92° F and the low 68° F, the average for use in the modified GDD calculation would be 86 + 68 = 154 / 2 = 77. The amount of precipitation listed on a climate report is the Liquid Equivalent Precipitation. This value includes the melted amount of any frozen precipitation (e.g., snow, sleet) that may have fallen in addition to any rain. Why is this frozen precipitation collected and then melted before being measured? The density of liquid water is constant; however, the density of frozen precipitation can vary greatly. One inch of "heavy" snow contains more water than one inch of "light" snow. Measuring the liquid equivalent of frozen precipitation can indicate the actual amount of water that fell, regardless of the type of precipitation. These values can also later be used in calculating ground water issues when snowmelt occurs. Sometimes people mistakenly try to determine the amount of water in a fresh snowfall by using a rule of thumb 10 to 1 ratio, assuming ten inches of snow melts to one inch of water. The problem with using this single ratio is that the density of snow can vary greatly from storm to storm and location to location. An extremely heavy, dense snow can have a ratio of only 3 to 1 (3 inches of snow melt to one inch of water), while very light snow can have up to a 100 to 1 ratio. That means only 1 inch liquid water can result in 100 inches of snow! Snowfall is the amount of fresh snow that has fallen during the 24-hour measurement period, while the snow depth is the total amount of snow on the ground and includes both old and new snow. Snowfall is measured to the nearest 1/10th of an inch while snow depth is measured to the nearest inch. Wind direction is measured in degrees, similar to reading a compass, and is reported as the direction the wind is blowing FROM. East = 90 degrees South = 180 degrees West = 270 degrees North = 360 degrees For example, if the wind direction is 45 degrees, the winds are coming out of the northeast and blowing towards the southwest. This would be called a northeasterly wind. A wind rose is a graphical representation of the wind speed and wind direction for a set of given dates at a particular location. The wind rose can be representative of the wind for a single month, a single year or a long-term average by month or year. There are two graphics for each wind rose. One graphic depicts the average wind speed by wind direction in miles per hour. The other graphic represents the percentage of frequency by wind direction. The Midwestern Regional Climate Center can generate wind roses for most major cities across the Midwestern United States. Tabular numeric data are also available. To find out further what wind roses are available, please contact the MRCC. A thunderstorm is considered severe if it produces wind gusts of 58 miles per hour or greater and / or hail æ inch in diameter or larger. Severe thunderstorm reports are archived by the National Climatic Data Center and are available from their online Storm Events Database at http://www.ncdc.noaa.gov/stormevents/. Preliminary storm reports are collected by the Storm Prediction Center http://www.spc.noaa.gov/climo/. For an official copy of a Storm Data publication, please contact the Midwestern Regional Climate Center or the National Climatic Data Center. The winds in a tornado are classified by the Fujita Scale, which was created by T. Theodore Fujita. The scale is based on observational studies of tornado damage paths. |Fujita Scale||Wind Speed (mph)||Expected Damage| |F-0||40 - 72||Light| |F-1||73 - 112||Moderate| |F-2||113 - 157||Considerable| |F-3||158 - 206||Severe| |F-4||207 - 260||Devastating| |F-5||261 - 318||Incredible| A watch indicates that conditions are favorable for severe weather to develop. You should remain alert for changing weather conditions and be ready to move to a place of safety. A warning means that dangerous weather is occurring or imminent and that you should seek safety immediately! Severe thunderstorm watches and tornado watches are issued by the Storm Prediction Center in Norman, Oklahoma. A watch may cover large portions of a state and will usually be in effect for a time period of 4 to 6 hours. Warnings are issued by your local forecast office on a county-by-county basis. Tornado and severe thunderstorm warnings are usually in effect for 30 to 60 minutes. Much of the data at the Midwestern Regional Climate Center comes from National Weather Service cooperative observing stations where an observer records the temperature and precipitation at the same time every day. A common observation time is 7:00 a.m. Precipitation measured at that time would be the total amount for the 24-hour period from 7:00 a.m. the day before to 7:00 a.m. the day of the observation. However, not all stations have a 7:00 a.m. observation time. Some record from midnight to midnight, producing a true daily record, while others may record in the evening. Cooperative station data from the Midwestern Regional Climate Center will be stamped with an observation time of "AM", "PM", or "MID" to indicate the time of day when the observation was recorded. Whenever possible, the actual time of observation will be noted on the data. The dew point temperature, wet bulb temperature and relative humidity all relate to the amount of moisture in the air. The dew point is the temperature to which the air must be cooled to reach saturation. The difference between the air temperature and the dew point temperature is proportional to the relative humidity. The closer the two temperatures are, the higher the relative humidity. When the air temperature becomes the same as the dew point temperature, the relative humidity reaches 100% and fog will develop and dew will form on surfaces. A common misconception is that the relative humidity cannot exceed 100%. In fact, this does occur but it is a temporary condition. The temperature can actually drop below the dew point, causing the air to become super-saturated. This condition is corrected quickly as moisture condenses into liquid to form fog or dew. As the water vapor in the air decreases, the dew point temperature decreases and the relative humidity returns to 100%. In the past, relative humidity was difficult to measure directly. An easier parameter to measure was the wet bulb temperature. This was found by placing a wet cloth over a thermometer, and then passing air over the cloth to evaporate the water. Initially, the evaporation of the water causes the temperature to decrease but the temperature eventually becomes constant. This steady temperature is called the wet bulb temperature and it relates to the amount of moisture in the air. It is then possible to calculate the dew point and relative humidity using the dry bulb and wet bulb air temperatures. These days, there are better methods for measuring relative humidity directly and there are few uses for the wet bulb temperature. In fact, it is unusual for the wet bulb to be measured directly anymore. It is now calculated from the air temperature and dew point or relative humidity.

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This is a nice easy read to introduce the students to the Dewey Decimal System. As I read this story, I have the students predicting what each level of the system represents. When the 500 level comes up, I always tell them that this is Bob’s favorite section. What do you think it is? I chose this story because I’m using the DDS throughout this lesson as a real life example of comparing and ordering decimals. To start the lesson, I’m going to use decimal grids to prove equivalency. Students have already used the grids to model. Now they will model to prove equivalency. As students are working through finding equivalent decimals, ask them what they notice about each decimal? I’m expecting to hear that by adding a zero to the next place values makes decimals equivalent. (SMP 8) I explain to students that using decimal equivalents helps us to compare and order decimals. Students need to know that when we compare decimals, we use the <, >, = symbols (SMP 6) In order to compare decimals, we have to line up decimal points. Ask the students why we line up decimal points? Students should notice that when the decimal point is lined up, so are the place values. Ask them why it is important to line up place values? Students should respond that we can only compare equal parts, just like fractions. Students that struggle can use their place value chart to help them line up the decimal place values. Students need to know that when they are asked to order decimals, they will be putting them in order from least to greatest or greatest to least (SMP 6) Ordering decimals is similar to comparing, but there are more decimals to compare. Again, we will use decimal equivalents to help us order decimals. Common misconception: Students will want to start comparing decimal places from the right and move left. Remind students that they need to start with the largest place value (left) because this will eliminate the largest number right away. Before moving on, ask the students this: Write down 5 decimals. Put them in order from least to greatest. Have students do a HUSUPU to share their decimals and ordering with a partner. Students can exchange papers with their partner and check each other’s work. This question allows students to work at their own level. Watch to see that students are lining up decimal points and annexing zeros to create equal place values. Ask your librarian to compile some books for you to use in class. Tell the students that they will need to put these books in order for the librarian. In order for all students to be able to experience this, give each student choose 3 books. They will need to put these three books in order according to the Dewey Decimal number and prove that their ordering is correct. Students will be applying what they have learned about comparing and ordering decimals to this task. As students are working on this task, walk around to make sure they are lining up decimal places, annexing zeros to create equal place values, and comparing the decimals starting with the largest place values. The worksheet is set up so that the students can work at their own pace. They can complete up to 3 investigations. (SMP 1,2,4,6) Have student write down in their own words why it is important to line up decimal places when comparing and ordering? Since students need to understand that the place value is what we are comparing they should say that by lining up the decimal points, lines up the place values. Then we compare the decimal places values largest to smallest.

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This is covered by: AQA 8035, Cambridge IGCSE, CEA, OCR B What Causes An Earthquake ? An Earthquake is a sudden tremor or movement of the earth’s crust, which originates naturally at or below the surface. The word natural is important here, since it excludes shock waves caused by French nuclear tests, man made explosions and landslides caused by building work. There are two main causes of earthquakes. Firstly, they can be linked to explosive volcanic eruptions; they are in fact very common in areas of volcanic activity where they either proceed or accompany eruptions. Secondly, they can be triggered by Tectonic activity associated with plate margins and faults. The majority of earthquakes world wide are of this type. An earthquake can be likened to the effect observed when a stone is thrown into water. After the stone hits the water a series of concentric waves will move outwards from the center. The same events occur in an earthquake. There is a sudden movement within the crust or mantle, and concentric shock waves move out from that point. Geologists and Geographers call the origin of the earthquake the focus. Since this is often deep below the surface and difficult to map, the location of the earthquake is often referred to as the point on the Earth surface directly above the focus. This point is called the epicentre. The strength, or magnitude, of the shockwaves determines the extent of the damage caused. Two main scales exist for defining the strength, the Mercalli Scale and the Richter Scale. Earthquakes are three dimensional events, the waves move outwards from the focus, but can travel in both the horizontal and vertical plains. This produces three different types of waves which have their own distinct characteristics and can only move through certain layers within the Earth. Lets take a look at these three forms of shock waves. Types of shockwaves Primary Waves (P-Waves) are identical in character to sound waves. They are high frequency, short-wavelength, longitudinal waves which can pass through both solids and liquids. The ground is forced to move forwards and backwards as it is compressed and decompressed. This produces relatively small displacements of the ground. P Waves can be reflected and refracted, and under certain circumstances can change into S-Waves. Particles are compressed and expanded in the wave’s direction. Secondary Waves (S-Waves) travel more slowly than P-Waves and arrive at any given point after the P-Waves. Like P-Waves they are high frequency, short-wavelength waves, but instead of being longitudinal they are transverse. They move in all directions away from their source, at speeds which depend upon the density of the rocks through which they are moving. They cannot move through liquids. On the surface of the Earth, S-Waves are responsible for the sideways displacement of walls and fences, leaving them ‘S’ shaped. S-waves move particles at 90° to the wave’s direction. Surface Waves (L-Waves) are low frequency transverse vibrations with a long wavelength. They are created close to the epicentre and can only travel through the outer part of the crust. They are responsible for the majority of the building damage caused by earthquakes. This is because L Waves have a motion similar to that of waves in the sea. The ground is made to move in a circular motion, causing it to rise and fall as visible waves move across the ground. Together with secondary effects such as landslides, fires and tsunami these waves account for the loss of approximately 10,000 lives and over $100 million per year. L-waves move particles in a circular path. Tectonic earthquakes are triggered when the crust becomes subjected to strain, and eventually moves. The theory of plate tectonics explains how the crust of the Earth is made of several plates, large areas of crust which float on the Mantle. Since these plates are free to slowly move, they can either drift towards each other, away from each other or slide past each other. Many of the earthquakes which we feel are located in the areas where plates collide or try to slide past each other. The process which explains these earthquakes, known as Elastic Rebound Theory can be demonstrated with a green twig or branch. Holding both ends, the twig can be slowly bent. As it is bent, energy is built up within it. A point will be reached where the twig suddenly snaps. At this moment the energy within the twig has exceeded the Elastic Limit of the twig. As it snaps the energy is released, causing the twig to vibrate and to produce sound waves. Perhaps the most famous example of plates sliding past each other is the San Andreas Fault in California. Here, two plates, the Pacific Plate and the North American Plate, are both moving in a roughly northwesterly direction, but one is moving faster than the other. The San Francisco area is subjected to hundreds of small earthquakes every year as the two plates grind against each other. Occasionally, as in 1989, a much larger movement occurs, triggering a far more violent ‘quake’. Major earthquakes are sometimes preceded by a period of changed activity. This might take the form of more frequent minor shocks as the rocks begin to move,called foreshocks , or a period of less frequent shocks as the two rock masses temporarily ‘stick’ and become locked together. Detailed surveys in San Francisco have shown that railway lines, fences and other longitudinal features very slowly become deformed as the pressure builds up in the rocks, then become noticeably offset when a movement occurs along the fault. Following the main shock, there may be further movements, called aftershocks, which occur as the rock masses ‘settle down’ in their new positions. Such aftershocks cause problems for rescue services, bringing down buildings already weakened by the main earthquake. Volcanic earthquakes are far less common than Tectonic ones. They are triggered by the explosive eruption of a volcano. Given that not all volcanoes are prone to violent eruption, and that most are ‘quiet’ for the majority of the time, it is not surprising to find that they are comparatively rare. When a volcano explodes, it is likely that the associated earthquake effects will be confined to an area 10 to 20 miles around its base, where as a tectonic earthquake may be felt around the globe. The volcanoes which are most likely to explode violently are those which produce acidic lava. Acidic lava cools and sets very quickly upon contact with the air. This tends to chock the volcanic vent and block the further escape of pressure. For example, in the case of Mt Pelee, the lava solidified before it could flow down the sides of the volcano. Instead it formed a spine of solid rock within the volcano vent. The only way in which such a blockage can be removed is by the build up of pressure to the point at which the blockage is literally exploded out of the way. In reality, the weakest part of the volcano will be the part which gives way, sometimes leading to a sideways explosion as in the Mt St.Helens eruption. When extraordinary levels of pressure develop, the resultant explosion can be devastating, producing an earthquake of considerable magnitude. When Krakatoa ( Indonesia, between Java and Sumatra ) exploded in 1883, the explosion was heard over 5000 km away in Australia. The shockwaves produced a series of tsunami ( large sea waves ), one of which was over 36m high; that’s the same as four, two story houses stacked on top of each other. These swept over the coastal areas of Java and Sumatra killing over 36,000 people. By contrast, volcanoes producing free flowing basic lava rarely cause earthquakes. The lava flows freely out of the vent and down the sides of the volcano, releasing pressure evenly and constantly. Since pressure doesn’t build up, violent explosions do not occur.

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This packet targets identifying numbers, representing numbers in a variety of ways, counting, and cardinality. What is included in this pack? These mazes ask students to identify numbers 1 through 20 by finding their way through the maze. There is an additional version that asks students to recognize a number in both its word and numeral form. These are made for numbers 1 to 10. Finally there is a make your own maze page for the students to make up their own maze! 2. Number Sorts: Students are exposed to the variety of ways a number can be represented. They need to identify and sort a variety of pictures, dominos, and ten-frames to match the corresponding number. 3. Counting Objects Mats (Numbers 4-20): These help students build one-to-one correspondence. The students count the objects on the mat and then clip a clothes pin or put a marker on the corresponding number. Students will work on counting objects and cardinality. 4. Ten-frame cards 1-20: Memory/ Go Fish: Students can build their recognition of numbers 1 to 20 by matching the numeral to the corresponding ten-frame. 5. Number of the day 1-20: The students practice writing the number with words, representing the number on a ten-frame, drawing a picture to match the number, and representing it on the number line. These could also be used in a grab bag station. The child would pull out a number or ten frame and line up that many objects next to the number card. For example, if the child pulls an 8 out of the bag, they would line up 8 pattern blocks next to the card. What can these resources be used for? -Number of the day -Independent or teacher directed math centers -Great for a Kindergarten unit on counting and cardinality -Intervention for First grade to build one-to-one correspondence

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More Science Worksheets A series of free Science Lessons for 7th Grade and 8th Grade, KS3 and Checkpoint Science in preparation for GCSE and IGCSE Science. Chemical Reactions and Equations Chemists use equations to describe what happens in a chemical reaction. The equations provide the essential information an an easy-to-read form. The simplest equations are word equations. The substances that take part in a reaction are called reactants. The substances that form as a result of the chemical reactions are called the products. reactants → products magnesium + oxygen → magnesium oxide Chemical names of compounds There are rules for how chemical names are built up. The first part of the name is usually the name of an element in the compound. The second part of the name has part of the name of the second element in the compound. If the element is not connected to other elements the suffix -ide may be added as in sodium chloride. Some more complex endings to compound names. SO4 - sulfate CO3 - carbonate NO3 - nitrate OH - hydroxide Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations. You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

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Theory of Continental Drift In geologic terms, a plate is a large, rigid slab of solid rock. The word tectonics comes from the Greek root “to build.” Putting these two words together, we get the term plate tectonics, which refers to how the Earth’s surface is built of plates. The theory of plate tectonics states that the Earth’s outermost layer is fragmented into a dozen or more large and small plates that are moving relative to one another as they ride atop hotter, more mobile material. Before the advent of plate tectonics, however, some people already believed that the present-day continents were the fragmented pieces of preexisting larger landmasses (“supercontinents”). The diagrams below show the break-up of the supercontinent Pangaea (meaning “all lands” in Greek), which figured prominently in the theory of continental drift — the forerunner to the theory of plate According to the continental drift theory, the supercontinent Pangaea began to break up about 225-200 million years ago, eventually fragmenting into the continents as we know them today. Plate tectonics is a relatively new scientific concept, introduced some 30 years ago, but it has revolutionized our understanding of the dynamic planet upon which we live. The theory has unified the study of the Earth by drawing together many branches of the earth sciences, from paleontology (the study of fossils) to seismology (the study of earthquakes). It has provided explanations to questions that scientists had speculated upon for centuries — such as why earthquakes and volcanic eruptions occur in very specific areas around the world, and how and why great mountain ranges like the Alps and Himalayas formed. Why is the Earth so restless? What causes the ground to shake violently, volcanoes to erupt with explosive force, and great mountain ranges to rise to incredible heights? Scientists, philosophers, and theologians have wrestled with questions such as these for centuries. Until the 1700s, most Europeans thought that a Biblical Flood played a major role in shaping the Earth’s surface. This way of thinking was known as “catastrophism,” andgeology (the study of the Earth) was based on the belief that all earthly changes were sudden and caused by a series of catastrophes. However, by the mid-19th century, catastrophism gave way to “uniformitarianism,” a new way of thinking centered around the “Uniformitarian Principle” proposed in 1785 by James Hutton, a Scottish geologist. This principle is commonly stated as follows: The present is the key to the past. Those holding this viewpoint assume that the geologic forces and processes — gradual as well as catastrophic — acting on the Earth today are the same as those that have acted in the geologic past. The belief that continents have not always been fixed in their present positions was suspected long before the 20th century; this notion was first suggested as early as 1596 by the Dutch map maker Abraham Ortelius in his work Thesaurus Geographicus. Ortelius suggested that the Americas were “torn away from Europe and Africa . . . by earthquakes and floods” and went on to say: “The vestiges of the rupture reveal themselves, if someone brings forward a map of the world and considers carefully the coasts of the three [continents].” Ortelius’ idea surfaced again in the 19th century. However, it was not until 1912 that the idea of moving continents was seriously considered as a full-blown scientific theory — called Continental Drift — introduced in two articles published by a 32-year-old German meteorologist named Alfred Lothar Wegener. He contended that, around 200 million years ago, the supercontinent Pangaea began to split apart. Alexander Du Toit, Professor of Geology at Witwatersrand University and one of Wegener’s staunchest supporters, proposed that Pangaea first broke into two large continental landmasses, Laurasia in the northern hemisphere and Gondwanaland in the southern hemisphere. Laurasia and Gondwanaland then continued to break apart into the various smaller continents that exist today. In 1858, geographer Antonio Snider-Pellegrini made these two maps showing his version of how the American and African continents may once have fit together, then later separated. Left: The formerly joined continents before (avant) their separation. Right: The continents after (aprés) the separation. (Reproductions of the original maps courtesy of University of California, Berkeley.) Wegener’s theory was based in part on what appeared to him to be the remarkable fit of the South American and African continents, first noted by Abraham Ortelius three centuries earlier. Wegener was also intrigued by the occurrences of unusual geologic structures and of plant and animal fossils found on the matching coastlines of South America and Africa, which are now widely separated by the Atlantic Ocean. He reasoned that it was physically impossible for most of these organisms to have swum or have been transported across the vast oceans. To him, the presence of identical fossil species along the coastal parts of Africa and South America was the most compelling evidence that the two continents were once joined. In Wegener’s mind, the drifting of continents after the break-up of Pangaea explained not only the matching fossil occurrences but also the evidence of dramatic climate changes on some continents. For example, the discovery of fossils of tropical plants (in the form of coal deposits) in Antarctica led to the conclusion that this frozen land previously must have been situated closer to the equator, in a more temperate climate where lush, swampy vegetation could grow. Other mismatches of geology and climate included distinctive fossil ferns (Glossopteris) discovered in now-polar regions, and the occurrence of glacial deposits in present-day arid Africa, such as the Vaal River valley of South Africa. The theory of continental drift would become the spark that ignited a new way of viewing the Earth. But at the time Wegener introduced his theory, the scientific community firmly believed the continents and oceans to be permanent features on the Earth’s surface. Not surprisingly, his proposal was not well received, even though it seemed to agree with the scientific information available at the time. A fatal weakness in Wegener’s theory was that it could not satisfactorily answer the most fundamental question raised by his critics: What kind of forces could be strong enough to move such large masses of solid rock over such great distances? Wegener suggested that the continents simply plowed through the ocean floor, but Harold Jeffreys, a noted English geophysicist, argued correctly that it was physically impossible for a large mass of solid rock to plow through the ocean floor without breaking up. Rejoined continents [48 k] Undaunted by rejection, Wegener devoted the rest of his life to doggedly pursuing additional evidence to defend his theory. He froze to death in 1930 during an expedition crossing the Greenland ice cap, but the controversy he spawned raged on. However, after his death, new evidence from ocean floor exploration and other studies rekindled interest in Wegener’s theory, ultimately leading to the development of the theory of plate tectonics. Plate tectonics has proven to be as important to the earth sciences as the discovery of the structure of the atom was to physics and chemistry and the theory of evolution was to the life sciences. Even though the theory of plate tectonics is now widely accepted by the scientific community, aspects of the theory are still being debated today. Ironically, one of the chief outstanding questions is the one Wegener failed to resolve: What is the nature of the forces propelling the plates? Scientists also debate how plate tectonics may have operated (if at all) earlier in the Earth’s history and whether similar processes operate, or have ever operated, on other planets in our solar system. CREDITS – USGS .

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But a new study in the journal Nature Geoscience concludes that this shallow strait between the North Pacific and the Arctic oceans has played a large role in climate fluctuations during recent ice ages. Depending on whether it's closed or open, the strait dramatically changes the distribution of heat around the planet. When sea levels decline enough that water can no longer flow from the Pacific to the Arctic through the strait, the North Atlantic responds by growing warmer. That warmth is strong enough to melt ice sheets and temporarily reverse the glaciation of the Northern Hemisphere. Generally, scientists think that changes in Earth's orbit around the sun have driven the repeated advance and retreat of glaciers during the Pleistocene — the period starting 2.58 million years ago and ending about 10,000 years ago. When less sun reaches the Northern Hemisphere during summer months, winter snows don't melt. The white snow reflects more of the sun's energy back into space, further cooling the region. Glaciers form and begin creeping southward. These ice sheets, a mile or more thick in places, suck up large quantities of water. Compared to today, sea levels dropped by as much as 400 feet during the Pleistocene. But while glacial periods follows Earth's orbital variations quite closely — they occur very roughly on 100,000-year cycles — for the past 100,000 years or so, a shorter warming and cooling cycle has played out over the larger one. Even as the amount of sunlight hitting the region diminished, parts of Greenland and North America warmed by nearly 3 degrees F. Glaciers then shrank and sea levels rose by up to 100 feet, only to reverse. This cycle repeated every few thousand years. Why? The authors argue that the Bering Strait, a choke point, is the critical factor. When sea levels dropped sufficiently, dry land emerged between North America and Asia. This dam halted the flow of water from the North Pacific into the Arctic. At present, about 800,000 cubic meters (211 million gallons) of water per second flow into the Arctic from the North Pacific. That's about 3.6 times the discharge of the Amazon, the world's largest river. This water from the north Pacific eventually flows to the north Atlantic. Water in the north Pacific is much fresher, and therefore much lighter, than the saltier water of the North Atlantic. And the influx of freshwater into the North Atlantic impedes a process that's critical to heat distribution around the globe. Scientists call this conveyor-beltlike flow the "meridional overturning circulation." And it's responsible for keeping Europe balmy compared to regions at similar latitudes elsewhere. When the overturning is impeded, however, the transport of tropical heat to high northern latitudes slows, and the north Atlantic grows colder. In other words, freshwater flowing into the north Atlantic can bring temperatures down in the region. Conversely, lessening the flow of freshwater into the north Atlantic can cause temperatures to rise. That's what the authors of this paper say happened repeatedly during the past 100,000 years. Here’s the cycle: Cooling brought on by changes in Earth's orbit caused glaciers to grow and sea levels to fall. Eventually, the seas dropped far enough that the Bering Strait was closed off. The flow of relatively fresh water from the north Pacific to the north Atlantic stopped, or was dramatically decreased. Without interference from this freshwater, the meridional overturning in the North Atlantic strengthened — by about 13 percent. Parts of Greenland, northeastern North America, and Europe warmed by 2.7 degrees F. Glaciers around thenNorth Atlantic then began melting. Meanwhile, as the northward flow of water in the Pacific was stymied, temperatures there dropped by the same amount — 2.7 degrees F. In the end, however, this warming was self-limiting. As increased warmth melted glaciers around the north Atlantic, sea levels began to rise. Eventually they rose sufficiently to again engulf the Bering land bridge. The flow of water from the north Pacific into the Arctic resumed. The meridional overturning in the north Atlantic again weakened. And the glaciers of the Northern Hemisphere again began advancing southward. None of this bears directly on the current trend of human-induced global warming. But it does indicate that scientists, enabled by ever-more powerful computers and more complicated — some might say "realistic" — climate models, are improving their understanding of Earth's climate system. It also highlights an important lesson: In complex systems (Earth’s climate), seemingly small changes, such as closing the 50-mile-wide Bering Strait, can have large consequences, like temporarily reversing a hemisphere-wide cooling trend. Or, as we talked about last week, a little warming might cause a lot more.

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Download the file ex1.pde and run this program. For the rest of the exercises in this session, you only need to edit the "draw" method in the file. The formula of a line between two points (x1,y1) en (x2,y2) is as follows: (x-x1)*(y2-y1) = (y-y1)*(x2-x1) 1.1 Write a function void drawLine(int x1, int y1, int x2, int y2) that draws a straight line between the given coordinates. While processing already provides a built-in function (named line), the goal of this exercise is to learn how to write such a function yourself, given the more primitive function "point". Change the "draw" method such that a line is drawn rather than the random noise. Make sure your function works for lines in all 4 quadrants. 1.2 Which variable (x or y) did you use as the dependent and which as the independent variable? Why is the choice of dependent and independent variable important? How do you determine which variable to use as the independent one? On older machines, arithmetic with floating point numbers was a lot slower than arithmetic with integers. Therefore, most drawing routines where speed was of the essence (such as a line drawing algorithm) avoided using floating point numbers in their calculations. 2.1: in your algorithm of exercise 1, change all integers (int) to double-precision floating point numbers (double). What effect does this have? Obviously, the algorithm no longer performs well because of rounding errors. The error can be illustrated by means of an example equation: x = (y/6) * 8 Imagine both x and y are of type int. If y = 2, then x will be 0 (so the error = 2,66 - 0 = 2,66). One way to decrease this error (i.e. increase the precision) is to multiply both sides of the equation by a factor 10. This gives the result 10x = 10*(2/6)*8 = 24, so x is equal to 24/10 = 2. The error now is 2,66 - 2 = 0,66. By increasing the factor with which both sides are multiplied (e.g. 100), the precision of the result will increase even more. The above method to work with floating point numbers solely by means of integer arithmetic is called fixed-point arithmetic. A regular floating point number (of type float or double) can be used to represent a very wide range of numbers using only a fixed bit size (32 resp. 64 bits). This is possible because the place of the decimal point (in dutch: de komma) in their representation can be at varying positions. If you only need a small range of values, you can represent a floating point number by an integer number by "fixing" the position of the decimal point. Imagine you want to represent floating point numbers with a precision of 2 numbers after the decimal point. Also imagine that you only need to represent decimal numbers of at most 4 digits. With 4 digits, you can normally represent integers in the range 0 to 9999 (using decimal arithmetic). If you want a precision of 2 digits after the decimal point, then with the same amount of digits, you can represent 0,00 up to 99,99. This range of values is considerably less, but you can now represent fractional numbers! The trick to fixed-point arithmetic is that we introduce an imaginary decimal point in the number, merely by programming convention (that is: by multiplying the number by 100 as in the first example). The computer does not know anything about this convention. For example, if we place the decimal point between digits 2 and 3 (as in the above example), then we represent the integer 5 by the actual integer 500 (because 500 = 0500 = 05,00 in our imaginary representation). A fractional number, such as 5,3 is represented by the actual integer 530 (because 530 = 0530 = 05,30). 21,65 is represented by the actual integer 2165, and so on. To turn an actual integer into a fixed-point integer, multiply by a "precision factor" (e.g. 100). To turn a fixed-point integer back into an actual integer, divide by the precision factor. The fixed-point numbers that we have been using thus far are said to be formatted as '2:2', meaning 2 digits before and 2 digits after the decimal point. Up to now, we have been working with decimal digits (that can take on a value between 0 and 9). In computer science, we mostly work with binary digits (taking on a value of either 0 or 1). So a binary 16:16 fixed-point number is an integer of 32 bits, where the 16 most significant bits represent the integer part and the 16 least significant bits represent the fractional part of a number. Notice that, whereas a normal unsigned int can represent values in range [0,2^32 - 1], a 16:16 fixed-point unsigned int can only represent values in range [0,2^16 -1]. Doing arithmetic with fixed-point numbers has the advantage that the computer is manipulating integers while we interpret them as fractional numbers. Addition and subtraction are trivial in fixed-point arithmetic. For example, in decimal 2:2 format 5 + 4 is represented as 0500 + 0400 = 0900, and 0900 is interpreted as 9. This also works for fractional numbers: 22,15 - 1,4 is represented as 2215 - 0140 = 2075, and 2075 is interpreted as 20,75. This works as long as you interpret the result of an operation in the same fixed-point format as the input arguments. Multiplication is less trivial. Consider 2,01 * 2,01. This is represented as 0201 * 0201 = 40401. While the two input arguments are 100x bigger than their interpretation, the output is 10.000x bigger (that is: 100a * 100b = 10.000ab). So either the output must be interpreted in the format 4:4 rather than 2:2 (i.e. 40401 = 00040401 ~ 0004,0401 = 4,0401) or you need to divide the result by 100 to convert it to 2:2 again (40401 / 100 = 404 = 0404 ~ 04,04). Note that because of this division, we lost 2 digits of precision (resulting in a rounding error of 0,0001). When dividing two fixed-point numbers, the problem of multiplication does not appear. When dividing 100a / 100b, the factor 100 is cancelled out. However, 100a/100b = a/b, which is no longer a fixed-point number (you lose all precision)! For example 5,4 / 2 is represented as 0540 / 0200 = 2 (integer division). To interpret the result as a decimal 2:2 fixed-point number again, you need to multiply by 100 again (2*100 = 200 = 0200 ~ 02,00). Notice that 5,4 / 2 ought to be 2,7, so we lost our precision. To avoid this, rather than calculating (a/b)*100, it is better to calculate (a*100)/b: (0540 * 0100) / 0200 = 270 = 0270 ~ 02,70 = 2,7! Notice that when multiplying or dividing fixed-point numbers, you have to be very careful for "overflows" in the intermediary results. If we only have 4 digits to store our decimal number, then we simply cannot store the intermediary number 40401 of the example multiplication. When multiplying two N:M fixed-point numbers, the result will have N+N:M+M digits. In the above examples, the results of multiplication and division were both 100x bigger than the representation of the input operands. When working with 32-bit numbers in a computer, be aware that fixed-point numbers which you multiply or divide can only have a maximum size of 16 bits. The first 16 bits can be divided into an integer and a fractional part, but the remaining 16 bits are required to store overflows. 2.2: apply fixed-point arithmetic to the formula of a line and integrate it in your algorithm. Turn the "precision" of your algorithm into a parameter. The other input parameters to the algorithm should remain unchanged and are still represented in integer screen coordinates. 2.3: in all of the above examples, I have been using decimal fixed-point numbers. Conversion between regular and fixed-point integers required multiplication or division by a certain decimal precision constant. There is, however, a more efficient way to do fixed-point arithmetic on a computer. When working with binary numbers, what precision factors would you choose? Why is this important? (hint: this factor is very easy to use when multiplying or dividing binary numbers). A downside of our line drawing algorithm is that it contains a lot of multiplications. On older computers, multiplication was a lot slower than addition or subtraction. We can remove some multiplications by taking the derivative of the equation of a line. For example, the derivative of 10x is 10. So, instead of calculating the y-value at each x-coordinate that we plot between x1 and x2, we can also calculate it once at x1, and then just increase the y-value by 10 as we move towards x2. That is: for each increment in the x-value by 1, we increment the y-value by the differential. For lines, the differential is constant and is simply the slope (dutch: richtingscoefficient) of the line to plot. To see why this works, consider the equation yk = mxk + b with 0 < m <= 1. When increasing x by 1, we get: yk+1 = mxk+1 + b yk+1 = m(xk+1) + b yk+1 = mxk + m + b yk+1 = yk + m Adapt your floating-point line drawing algorithm to use this technique, which is called a Digital Differential Analyzer. Write a line algorithm using fixed-point arithmetic with 16 bits of precision and that uses DDA to save on the number of multiplications. Make sure it works in all 4 quadrants. This algorithm must not use floating point arithmetic. Bresenham's algorithm is a well-known line drawing algorithm and is very efficient as it only uses integer addition, bitshifts and equality tests involving 0. Given 2 points, Bresenham's algorithm draws a line by at each step making a choice between one of two pixels to plot. It chooses the pixel that is closest to the 'real line'. Consider two points (x1,y1) and (x2, y2). Imagine (x1,y1) is the starting point. Given this pixel, there are 8 possible choices to plot the next pixel. It should be clear that only 2 of these 8 neighbouring points are relevant when drawing a line in the direction of (x2, y2). In what follows, consider 0 <= m <= 1 and x1 < x2 (in other words: the line is being drawn in the first octant). We consider x as the independent variable, which we increase by 1 at each step. Imagine that during iteration k we are plotting the point (xk, yk). What is the next 'ideal' point? The ideal point would be (xk+1, y) with y = m*(xk+1) + b. However, this is a fractional number which we cannot represent on our discrete screen. The two pixels that are the best approximation to the real point are (xk+1,yk) and (xk+1, yk+1). The first is the point directly to the right of the current point. The second is the point to the right and above the current point (cf. the figure below). So which of these two points should we plot during the next iteration? To summarise: Bresenham's algorithm at each step must make a decision between plotting (xk+1, yk) or (xk+1,yk+1), given that the ideal point to plot would be (xk+1, m*(xk+1)+b). To make this decision, we calculate the error rate of both choices, which we can define as their distance to the ideal point. As indicated in the figure we can then define: Distance between "right-point" and "ideal point" = d1 = y Distance between "right+above point" and "ideal point" = d2 = (yk+1) - y We can then decide between these points by checking whether (d1 <= d2). If d1 <= d2 then we plot (xk+1,yk) during the next iteration, otherwise we plot (xk+1,yk+1). However, calculating these variables at each iteration is not going to result in an efficient algorithm. To speed things up, we introduce a "decision variable" which will be updated at each iteration. First of all, we rather test the sign of (d1-d2) rather than d1<=d2 because a comparison with 0 may be faster. Hence, if (d1-d2) > 0 choose (xk+1,yk+1), otherwise (xk+1,yk). (d1-d2) = y - yk - ( (yk+1) - y) ) = y - yk - (yk + 1) + y. Recall that y = (m*xk+1)+b, so by substitution: (d1-d2) = m*(xk+1) + b - yk - (yk+1) + m*(xk+1) + b = 2m * (xk+1) - 2yk + 2b - 1. Replacing m by dy/dx (with dy = |y2-y1| and dx = |x2-x1| ) we get: (d1-d2) = 2*(dy/dx)*(xk+1) - 2yk + 2b-1 = 2*(dy/dx)*xk + 2*(dy/dx) - 2yk + 2b - 1. This is a complex equation which we can simplify by multiplying both sides with dx. Multiplying by dx has no result on our test since dx is always positive, such that the sign of d1-d2 will not change. Pk = dx*(d1-d2) = dx * ( 2*(dy/dx)*xk + 2*(dy/dx) - 2*yk + 2b - 1 ) = 2dy*xk + 2dy - 2dx*yk + 2dx*b - dx = 2dy*xk - 2dx*yk + c (with c = 2dy + dx(2b - 1) ) We now have our decision variable which can be calculated relatively efficiently. However, in its current form we still need to calculate it at each iteration. We can change this by only calculating the incremental differences between Pk and Pk+1. We can do so because changes in Pk are linear. So we calculate: dP = Pk+1 - Pk = 2dy*xk+1 - 2dx*yk+1 + c - 2dy*xk + 2dx*yk - c = 2dy*xk+1 - 2dy*xk - 2dx*yk+1 + 2dx*yk = 2dy*(xk+1 - xk) - 2dx*(yk+1 - yk) = 2dy - 2dx(yk+1-yk) Because we increase the x-value by 1 at each step, xk+1 - xk = 1. The value of (yk+1-yk) is less trivial, since it depends on the choice of the point. (yk+1-yk) = 0 if we choose (xk+1,yk), = 1 otherwise. So eventually, we get: dP = 2dy - 2dx*(0) = 2dy when choosing the "right-point" dP = 2dy - 2dx*(1) = 2dy - 2dx when choosing the "right+above point". So now we know how to increase Pk to arrive at Pk+1 during each iteration. Such an addition is much more efficient than calculating Pk every time (cf. the DDA technique presented earlier). All that is left to define is the initial value of P, i.e. P0. Pk = 2dy*xk - 2dx*yk + 2dy + dx(2b - 1) P0 = 2dy*x0 - 2dx*y0 + 2dy + dx(2b - 1) b = y - mxk we get: = 2dy*x0 - 2dx*y0 + 2dy + dx*(2*(y0 - (dy/dx)*x0) - 1) = 2dy*x0 - 2dx*y0 + 2dy + 2dx*(y0 - (dy/dx)*x0) - dx = 2dy*x0 - 2dx*y0 + 2dy + 2dx*y0 - 2dy*x0 - dx P0 = 2dy - dx We now have an initial test value for P. Depending on whether or not P is bigger than 0, we choose one of 2 points to plot during the next iteration. In addition, the test also determines how we have to update P for the next iteration. Given the above calculations, implement Bresenham's algorithm for lines in the first octant. When you got this working, extend your algorithm to work for arbitrary octants.

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Diction is the style of writing that a specific text uses; it's determined by the types of words a writer chooses. Writers use a particular kind, or form, of diction to reflect their vision to their readers. The consistent use of diction helps to enable readers to fully participate in the writer’s world. Formal diction refers to word usage that’s commonly found in formal scenarios, and it doesn’t necessarily reflect the way people speak. Such situations can include language in presentations, formal gatherings and scholarly journals. This form is mostly used in situations that address highly educated audiences. Formal diction, also called elevated language, often uses more abstract or figurative words, and it privileges words with Latinate roots, such as “edify” and “beguile.” Formal diction uses elegant, extravagant and sophisticated vocabulary, and the words generally are polysyllabic, meaning they have more than one syllable. Informal diction is word usage that is grammatically correct but appropriate for more informal settings. This kind of language is commonly used when addressing a familiar or a more comfortable specific audience, such as your friends, and you can use this diction in personal letters or documents with a conversational or entertaining tone. Informal diction includes slang and colloquial diction; slang uses newer words that can be impolite, and colloquial speech uses words commonly found in everyday speech. Such language might use the word “wise up” instead of “edify” and “jerk your chain” in place of “beguile.” Along with slang and colloquial diction, vulgarity is also a form of informal diction -- that is, language lacking in taste and refinement. Standard diction is closely related to informal diction, but with minor differences. Such diction is often used when addressing a well-educated audience; it's the level used for college papers and business communications. Instead of using the slang term "wise up," standard diction would use “learn.” Standard diction is also referred to as Standard American English. Connotations are a key element of diction, as they are used to suggest and display emotional meaning. A connotation can give the listener or reader an impression that's created by their associations with a word rather than by its dictionary definition. This type of diction can be broken into two types of connotations, positive and negative. A positive connotation can help leave the audience with a positive attitude while a negative connotation will do the opposite.

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I begin by asking the students to draw on their graph paper two triangles: When all have completed this, I ask them to compare their triangles with their neighbor's. Hopefully, the students will respond that their right triangles with legs 4 and 5 are congruent. We will generally spend a couple of minutes in discussion of the question: Why are all of these right triangles congruent? Then, we will focus on the triangles with angles of 30 degrees and 90 degrees. I'll ask, "Are all of the triangles congruent in this case?" This can get interesting because there will have been some congruent triangles as well as some that are similar, but not congruent. After all of the students begin to realize that not all of the triangles are congruent, I will ask, " If they are not congruent, then what can we say about the triangles that were created in this case?" Hopefully, the students will remember their recent work with similar polygons and they will respond that everyone’s triangles are similar. Either way, I will follow this with a discussion of the Angle-Angle Similarity Postulate, including a discussion of why just two angles are required and not three. To close out this activity, I will directing the students back to their graph paper. Then, I will ask them to draw two more triangles: Since my students are expected to know the Pythagorean Theorem at this point, I will also ask them to find and label the lengths of the hypotenuse of each triangle. Once the students complete their drawings, I will ask, "What is true about these two triangles? What can we say about the relationship between the sides of these triangles?" My hope is that it will not be a big leap for my students to conclude that the corresponding sides of these similar triangles are all in the same ratio. In this section we will work more formally with the idea of similar figures. I begin by handing outthe worksheet entitled Introduction to Similar Triangle Proofs. We will briefly discuss the rules written at the top on the page. The Cross-Product Property was used by the students in previous lessons, and should need little discussion. Someone usually asks at this point why, in the second and third statements that we look at, line segment symbols are not used and why there are equal signs, rather than congruent symbols. These are great questions, and provide an opportune moment to revisit the subtle differences in a segment's name and its measure. I then ask the students to work on the first proof, filling in the missing statements and reasons. As always, I remind them to mark their diagrams using colored pencil as they write in their ‘givens’ and find congruent angles or segments! This really helps students to see the information that they are working with, and is a huge aid in naming the triangles correctly. When the majority of the students have completed the proof, we discuss the students’ arguments, and continue this same process with each of the remaining proofs. The last proof asks the students to prove a product. I have found that the step in which they must set up a proportion is particularly difficult for students. I encourage them to work backward from the products that they are asked to prove equivalent - make sure that the first two factors will multiply together in their proportion (one in the numerator of the first fraction, the other in the denominator of the second fraction, and then the last two factors can go in either of the remaining places). This seems to help. A proof, with no hints included in it, is handed out. If there is more than a minute or two, I may decide to give students the proof as a Ticket out the Door. I'd prefer this, since it will leave me with a good sense of student understanding of the day's lesson. If time is limited, I will give the students the proof for homework and I will collect it upon their arrival the next day. In this case, I remind the students to refer back to the day’s worksheet on similar triangle proofs as they do the homework. The students are also working on their Create Your Own Similar Figures Projects for homework.

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Transposases shift genes around in the genome In the 1940's, Barbara McClintock discovered that the genome is a dynamic, changing place. She was studying maize, and she found that the beautiful mosaic colors of the kernels did not follow typical laws of inheritance. When she looked inside the cells, she found that the chromosomes changed shape, swapping pieces from one chromosome to the next. From this work, she found that the color changes were caused by the removal of a particular piece of DNA from the general area of the gene that caused the color, allowing the gene to be expressed and create pigments. She called this process transposition, where a piece of DNA is cut out of one place and pasted into another location. Since then, transposing DNA has been found in organisms of all kinds. In our cells, it is normally a rare process, but careful analysis of our genome shows that fully 40 percent of the genome has moved around in the distant past. Bacteria have more active transposable elements, which shuttle genes for antibiotic resistance around. But by far the most active form of transposition is performed by retroviruses, such as HIV, that multiply by inserting themselves into the DNA, and then forcing the cell to make many new copies of their genetic information. In the simplest cases, transposition needs only two things: a transposon (the DNA that moves), and a transposase (the enzyme that cuts out the DNA and moves it to a different place). The enzyme shown here is a bacterial transposase (PDB entry 1muh ) that moves a transposon called Tn5. The Tn5 transposon is a piece of DNA that includes several genes for antibiotic resistance, along with the gene needed to build the transposase itself. The crystal structure has caught the enzyme in the middle of the process of transposition. The process starts when two copies of enzyme bind to the DNA at the two ends of the transposon. Then, the two ends are brought together, closing the transposon into a big loop, and the transposase cuts the DNA at both ends. This is what we see in the structure: two copies of the enzyme holding the two severed ends of the DNA (note that the actual loop of DNA is much larger...5700 base pairs long). Finally, the enzymes find a new location on the DNA and reinsert the transposon. Transposition is a double-edged sword, with benefits and dangers. Our DNA is filled with mobile DNA sequences, so there has obviously been a lot of action over the course of our evolution. Some people propose that mobile DNA is completely selfish--it starts hopping around the genome, copying itself, and there's no way for our cells to stop it. This is certainly the case with viruses like HIV--they selfishly use the cell as an incubator to reproduce, providing no benefit to the cell or to the infected person. However, mobile DNA is a slow but potent source of mutation, so it may have provided a method, over millions of years, to shuffle and rearrange the genome, providing the diversity that drives evolution. Our genome is currently filled with many old, inactive mobile elements, left as a legacy of our gradual evolution. A Tetrameric Transposase Transposases use many different mechanisms for cutting and pasting DNA. This one, the lambda integrase from a bacteriophage (PDB entry 1z1g ), uses a more complex mechanism than the Tn5 transposase. This structure again catches the enzyme in the middle of its reaction, which involves an elaborate looping of DNA in and around the enzyme. In the process, an X-shaped Holliday junction is formed inside the enzyme, as shown in the lower illustration. Exploring the Structure Many transposases have a signature active site that includes three acidic amino acids, termed the DDE group. The active site of the Tn5 transposase is shown here, from PDB entry 1mus . The DNA is shown at the top in spacefilling spheres, and the three acidic amino acids are shown with balls-and-sticks. The acidic amino acids hold two metal ions, shown here in green, that assist with the cleavage and reconnection reactions. This illustration was created with RasMol. You can make similar pictures by clicking on the accession codes here and picking one of the options for 3D viewing. Related PDB-101 Resources - L. Haren, B. Ton-Hoang and M. Chandler (1999) Integrating DNA: transposases and retroviral integrases. Annual Review of Microbiology 53, 245-281. - Mobile DNA II, edited by N. L. Craig and others, ASM Press, 2002. - M. J. Curcio and K. M. Derbyshire (2003) The ins and outs of transposition: from mu to kangaroo. Nature Reviews, Molecular and Cellular Biology 4, 1-13. - M. Steiniger-White, I. Rayment and W. S. Reznikoff (2004) Structure/function insights into Tn5 transposition. Current Opinion in Structural Biology 14, 50-57. December 2006, David Goodsell

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- Help early learners develop essential reading readiness skills while they learn their alphabet. - This revised edition is your ultimate resource for teaching letter names and sounds! - Over 200 pages of engaging activities help students see, hear, say, and write the 26 letters of the alphabet while they develop the important reading readiness skills of alphabetic awareness, print awareness, phonemic awareness, and visual discrimination. You'll love Jumbo Fun with the Alphabet because it: - comes with over 200 pages of curriculum-correlated alphabet activities. From 3D art and craft projects to reproducible trace and write pages, there are a variety of activities to help your students see, hear, say, and write all of the 26 letters of the alphabet. - develops the four basic readiness skills students need before beginning formal reading. Activities are thoughtfully designed and consistently repeated to help students master alphabetic awareness, print awareness, phonemic awareness, and visual discrimination. - contains activities that help students exercise fine motor skills as they learn their ABCs. Students are asked to draw, trace, write, color, cut, fold, and glue as they learn letter names and sounds. Activities also provide extra practice in listening and following directions. - features brand-new teacher pages that help you introduce letters with ease. Teacher pages offer simple suggestions to help you introduce students to each letter of the alphabet and implement each activity. Activities incorporate the four language domains to engage students in the instruction and practice of each letter of the alphabet. - Hear It! - Students practice identifying letters and hearing them in spoken words. After a short discussion, a reproducible worksheet is provided that asks students to recognise and identify the sounds of the new letters. - Draw It! - Students are given step-by-step directions to draw objects or animals that start with the letters they're practicing. Drawings use simple shapes to create the images and give students opportunities to add their own creative details. - Write It! - Students practice tracing and printing uppercase and lowercase letters. There's also a fun dot-to-do activity to reinforce coordination and number skills. - Read It! - Each letter has a four-page fold-up book that provides students with short stories they can read on their own in class or at home. Stories help students practice a variety of readiness skills such as distinguishing letters from words, locating a printed word on a page, matching print to speech and moving from top to bottom and left to right on a printed page. - Make It! - A fun art project complete with pictorial directions engages students as they put together their own alphabet-inspired creation. The instruction in Jumbo Fun with the Alphabet focuses on the four basic readiness skills that all students need to master before moving on to a formal reading program. - Alphabetic Awareness - To become of a successful reader, students must know the names, shapes, and forms of all 26 letters of the alphabet. Jumbo Fun with the Alphabet helps students achieve this goal by introducing them to the letters of the alphabet using engaging, illustrated animals whose names start with the featured letter such, as ant, bear, cat, and so on. The animal becomes a common thread throughout the activities for that letter, facilitating both sight and sound recognition. - Phonemic Awareness - Realising that words are made up of sounds and hearing those sounds in spoken language are important steps in reading readiness development. 'Hear It!' and 'Draw It!' lessons provide this essential practice by asking students to recognise and identify beginning sounds through reproducible art and matching activities. - Print Awareness - Beginning readers need practice distinguishing the difference between a single letter, a word, a sentence, and a story. The simple story inside each 'Read It!' mini storybook introduces important concepts-of-print skills while further reinforcing letter and sound recognition. - Visual Discrimination - Students are given multiple opportunities to view the letters of the alphabet and to practice making them. The 'Draw It!,' 'Write It!,' and 'Make It!' activities engage students in visual discrimination practice while they practice drawing and following directions. Ideal for Grades PreK-1

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Beacon Lesson Plan Library Marion County Schools Help students grasp the difficult concept of using quotations. This lesson uses a hands-on approach to assist students in mastering this skill in a fun and easy way! The student uses conventions of punctuation (including but not limited to, commas in a series, dates, and addresses; quotation marks to indicate dialogue; apostrophes to indicate singular possession; periods in abbreviations). -Sentence strips or long pieces of white paper -Elbow shaped macaroni -Plastic baggies (one for each student) -Quotation Worksheet (see Associated File) -Rubric (see Associated File) 1. Have macaroni separated into plastic baggies ready to distribute. 2. Gather additional materials. NOTE: This lesson only teaches quotation marks. 1. Explain to students that conversations take place within many sentences. Writers use quotations to show when the person is talking. Show students a selection in their reading books or a book from the media center that has conversation. Point out the quotation marks. At this time, distribute blank sentence strips to students. 2. Put the following sentence on the board or overhead for the students to copy onto their strips of paper: We love to learn said the students. Distribute a bag of macaroni and glue to each student. 3. Discuss with students that where the quotations begin and end marks exactly what the students said. Ask students to tell you exactly what words were said. Add the quotations onto the sentence and instruct the students to glue macaroni onto their copied sentences to match where the quotations are. Circulate to make sure students are correct. 4. Emphasize to students that where the quotations begin and end mark exactly what the students said. 5. Give the students another sentence and sentence strip to continue to practice using quotations. Ask them to silently read it and then to decide exactly what words were spoken. Point out that these words are the ones to be placed inside the quotation marks. 6. Walk around the room while the students are working and assist them in this processs. Allow for peer editing from students who are competent before gluing. Offer feedback and guidance as necessary. 7. Continue providing practice and feedback until you feel that students understand how to use quotations. Provide students with the worksheet in the Associated File to assess them formatively. NOTE: This lesson only assesses quotation marks. Students are formatively assesed based on the attached assignment titled Quotation Worksheet (see Associated File). Use the Rubric (see Associated File) to assess students on their ability to add quotations to five different sentences. Students may use beans as puncuation. The macaroni may be used as commas. File Extension: pdfQuotation Rubric File Extension: pdf

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This is a fun activity that requires students to recognize place value and be able to read and comprehend number words. It is easily adapted to lower values or higher values depending upon learning objectives and targets. This is a Template Preview link. You will only be able to see the presentation slide. You will see only the main activity slide and not the drag and drop pieces or the directions which are located in the work space and in the presenter’s notes. To view the entire activity, please click Use Template and then edit your copy to meet the needs of your learners. 2.b.2.B Number and operations. The student applies mathematical process standards to understand how to represent and compare whole numbers, the relative position and magnitude of whole numbers, and relationships within the numeration system related to place value. The student is expected to use standard, word, and expanded forms to represent numbers up to 1,200. Latest posts by Lindsay Foster (see all) - BISDLearnTech Resource Templates *NEW* - November 28, 2018 - Discovery Education Activity For the Holiday Season - November 27, 2018 - TCEA Hosts Virtual Live Chat with Santa - November 27, 2018

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For this portion of the lesson, you will need a set of card with the 6 basic Plane Shape Cards (square, circle, rectangle, diamond, oval and rhombus). Every student will need a piece or string about 2 feet long. I cut and keep the yarn from year to year. I distribute the yarn to the students and I say to the students, We are going to review some of the shapes that we have already covered and we will also be learning about two new shapes. We are going to use this string to practice creating some shapes. I am going to say a shape and I want you to try to make that shape out of your string. I say the shape and have them try making it. I then hold up the card with the shape to give visual support if needed and for the children to check their work. I finish by asking the students to make an oval and a rhombus. The children know what an oval is, but they are perplexed by the request for a rhombus. I hold up the picture, the students say....Oh! A diamond. I collect the string and have the students take their seats at their Smartboard spots to begin our instruction. For this portion of the lesson, I use my SMART Board. If you have a SMART Board, the file Oval and Rhombus can easily be downloaded and opened. If you have a different type of interactive whiteboard, you can still use this lesson by opening the file in Smart Notebook Express. There is also a PDF of the slides so you can recreate this part of the lesson. I gather my students in front of the SMART Board. I have cards with each student's name printed on. These cards are used for selecting who will come up to the SMART Board. I open the first slide (SMART Board Slide 1) with the lesson objective written in "student friendly" terms. There is a content objective and a language objective to help focus on vocabulary expansion for my English Learners (ELs) to be congruent with SIOP instructional techniques I read these objectives aloud for my students. Content Objective: I can identify the characteristics of ovals and rhombuses (diamonds) and determine if a shape is an oval or rhombus. Language Objective: I can tell a friend whether a shape is an oval or a rhombus and why. We progress then progress through the rest of the slides. Slide 2: This is an oval. Slide 3: An oval is like a circle, but the points around it are not all an equal distance to the center. I point out how on some parts of the line I am far away from the center and on other parts I am very close. Slide 4: Let's sort some shapes!! I invite students up to the SMART Board to slide shapes into the correct section. I make sure that the students tell why the shape they moved goes where it goes. This supports Common Core Standard for Mathematical Practice #3, (Construct viable arguments and critique the reasoning of others). I want the students to be able to support why they classified a shape. Slide 5: This is a rhombus. We also call it a diamond. Slide 6: With a rhombus, all four sides are equal. One set of corners has small angles, the other has big angles. I hold my hands over each corner to show the students how my hands are far apart on two angles and closer together on the other two. Slide 7: Is this a rhombus? Why or why not? I explain to the students that two sides are short and two sides are longer. A rhombus must have four equal sides. Slide 8: Let's sort some more shapes!! Again, the students need to tell why they placed the shape where they did. Slide 9: Let's sort again, but this time let's include both the rhombus and the oval. The students continue telling why they moved the shapes where they did. Slide 10: It is now Turn and Talk Time. My students love this opportunity to practice their academic vocabulary. This is especially important for my English Language Learners. I have the students hold hands in the air with their designated Turn and Talk partner. I then ask them the question, What shapes do you see here? How many? How do you know? The students start their conversation and I am impressed by what I hear. I note that several students realize there are 5 rhombuses. The students are also discussing if two of the boxes together make a rhombus, but I hear them say, that all four sides would not be equal. After they are done with their conversation, I invite a student to come up to the board and share the discussion he had with his partner. The students explains to the class that there are 5 rhombuses. He tells the class how he knows they are rhombuses. I do not interject into the conversation because the student did a great job explaining to the class. The students take their seats at their tables to begin guided practice. For this portion of the lesson, you will need the Oval and Rhombus Real World Shape Sort. I print the cards on a colored printer and laminate for durability. I printed four sets of the cards, so there was one set for each table of students in my classroom. The cards should be cut apart. I distribute each set of cards to the tables face down. I pass the cards out around the table so each student gets at least two cards. I then place one set of the larger cards that are labeled rhombus and oval at each table. I say to the students, we are going to sort some things that we find in our word as ovals and rhombuses. You will go around the table and hold up just one of your shapes. You will say what it is and what shape it is. For example, if I have a picture of a kite, I would say, "The kite is a rhombusl". Then place the shape next to the sign that has the circle on it and the next person goes. I want everyone to say the sentence. Don't just put your card down. Keep going around the circle until all of the cards are laid down. The students begin the activity. I circulate around the room to make sure they are sorting the shapes correctly. Because I want my English Language Learners to expand their vocabulary I make sure the students are saying the sentences that describes their shapes. I assist students by naming objects they are not familiar with as well. I check the students sorted cards. The students pick up the cards and we prepare for independent practice. For this section of the lesson, you will need student copies of the Oval and Rhombus Sorting Activity included in this lesson. I pass the activity sheets out to the students and have them put their names on the top of their papers. I then explain to the students, We will be sorting some objects by shape. You will be deciding if the shapes are circles or triangles. I want you to cut apart the shapes and place them on the correct sections of the paper. Do not glue until you have raised your hand for me to check our paper. The students begin there work as I move around the room, checking their work. I make sure to check in with my English Language Learners and have them name the different objects that they are sorting. I correct any mistakes that the students may have made. After they have glues the objects down, I have them place the paper in their mailbox.

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Solving word problems takes skill, attention to detail, and a good problem solving strategy. Fourth grade math word problems usually involve one of the basic math operations – addition, subtraction, multiplication, or division. It is not uncommon to see two operation types in one problem, but generally speaking there is often only one operation involved. The word problems themselves require either a one or two step calculation to correctly solve the question, and they are characterized by real world scenarios familiar to a 4th grade student. A one-step problem may be as simples as, "Jack has $4.25 and Kayla has $3.80. How much money do they have altogether?" This straightforward problem merely requires the students to add the two amounts of money together. At the beginning of fourth grade, this would be an appropriate example of 4th grade math word problems. A more advanced one-step problem would be, "A friend tells you that they will be 405 weeks old on their next birthday. How old is that in years?" Two-step word problems require more effort. For instance, "Michael ate 12 cookies, while his sister ate 9 cookies. If mom baked 56 cookies, how many are left?" Again this would be a word problem students may encounter at the beginning of 4th grade. More taxing problems could include the likes of, "A sign before a bridge says 'weight limit 2 Tons.' The pickup truck weighs 1,675 lb, and has a bag of sand that weighs 400 lb in the back. The driver weighs 175 lb. Should he drive the truck across the bridge?" There are many different strategies for solving this type of problem, but the one that I have had the most success with is a four-step problem solving strategy. - Understand: What are you being asked to find out? Students need to identify the outcome of the problem and keep this in mind as they are working towards a solution. - Plan: What are you going to have to do to solve this problem? Will you need to guess and check? What operation(s) are involved? Will you draw a picture to help you? Can you make an estimate? - Solve: If the plan is sound, then this is the stage where you put it into action - Check: Look at your answer. Does it answer the question? Is it a reasonable answer? Is there a way to check and see if your answer is correct? A good place to find examples of 4th grade math word problems is the Primary Resources website. Here you will find a selection of free PDF, Word, and SMART Notebook files to download. It is an English site, so the equivalent US grade level is Year 5, but feel free to move up and down a grade to suit the abilities of your children. SMART Board users should also check out the resources on the SMART Exchange website. It has a selection of problems and teaching strategies for download. Abcteach.com also has another reasonably good selection of word problems that you can print out. If copyright allows, you can also run some of these PDFs through a free converter like www.pdftoword.com and then you will be free to edit any of the numbers to suit your needs. Word problems are relatively easy to differentiate by just changing the numbers in the story – larger numbers for the more gifted children, and smaller numbers for your less able students. You can also add or remove steps. One step problems are less work, and easier to solve, than two-step problems, so save those for your lower ability students, and add steps to challenge your gifted and talented children. 4th grade math word problems may seem like a chore to some students, but practice and perseverance is the keys to success. For more information on what is taught in 4th Grade Math, read 4th Grade Skills: What Every 4th Grader Needs to Know.

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When content behaves in an intuitive, logical and predictable way, learners can focus more of their energy and attention on understanding rather than on the mechanics of the user interface. Understanding can also be supported through the use of language that is appropriate for the audience’s reading level, as well as explanations of new or unfamiliar content and features (acronyms and abbreviations, subject-specific jargon and idioms). This will make the content more accessible not only to learners who have cognitive and learning challenges, but also to learners with limited English proficiency. The W3C video entitled Understandable Content examines the importance of plain language and clear design in more detail. The following techniques will help you make your content understandable: - Clarify expectation through clear directions and models - Follow conventions and strive for consistency - Use plain language - Identify the language The techniques are also summarized in a table with the corresponding Web Content Accessibility Guidelines for your reference. |Technique||Benefits Learners Who Are||Relevant WCAG Guidelines| |Clarify expectations through clear directions and models||Have learning or cognitive disabilities||3.3.2 Labels and Instructions (A); 1.3.3 Sensory Characteristics (A)| |Follow conventions and strive for consistency||Have cognitive disabilities||3.2.3 Consistent Navigation (A); 3.2.4 Consistent Identification (A)| |Use plain language||Have learning disabilities||3.1.3 Unfamiliar Words (AAA); 3.1.4 Abbreviations (AAA); 3.1.5 Reading Level (AAA)| |Indicate the document language||Blind or have learning disabilities and use text to speech||3.1.1 Language of Page (A); 3.1.2 Language of Parts (AA)| Access for all people, including people with disabilities, to web environments.View in glossary Artificial production of human speech, using special software and/or hardware.View in glossary Clarify expectations through clear directions and models Before learners are asked to respond, make sure you provide clear directions for what is expected in their answers: length requirements, citation formats, and so on. Whenever possible, link to a rubric (and an exemplar if one is available) to help clarify expectations. Finally, review your directions to make sure they don’t rely on sensory characteristics such as color, shape, position or size. Not all of your readers may be able to perceive these characteristics, and the directions will not make sense to them if that is the case. An example would be asking the reader to “review the passage to the right before answering the question.” A screen reader would not inform the reader of the location of the passage on the page, and the reader could be confused as to which passage the question references. It would be better to instruct the reader to “review the passage labeled ‘Theory of Thermal Equilibrium’ before answering the question.” The label would provide an additional cue that does not rely on visual perception. Follow conventions and strive for consistency Consistency, in both the structure and formatting of the information, can help learners understand how the content works. Conventions can also aid with usability. One example of a convention that is familiar to most learners is the use of underlining to indicate hyperlinked content. Underlining content that is not meant to be a hyperlink (or vice versa, removing the underline from hyperlinks) may prove confusing. If the content includes recurring features that are unique to it, consider including a “how to use this resource” section at the beginning that explains the meaning of special icons and other unique features. This will enhance usability for all learners. Use plain language Use language that is appropriate for the reading level of your audience to make the content easier to understand. Sites such as Hemingway Editor will help you identify the reading level of your content. They will also suggest simpler, shorter sentences. To help those who are new to the topic, either provide a glossary at the end or link to online definitions of unusual words or phrases. This includes jargon and idioms that may be unfamiliar to some readers. Also, expand acronyms and abbreviations the first time they are used. For additional information on the use of plain language,visit the following sites: - Top Ten Principles for Plain Language (National Archives) - Federal Plain Language Guidelines (Plainlanguage.gov) Identify the language Identifying the language will help screen readers select the correct voice and pronunciation rules. This is especially important if the content includes more than one language, as listening to the foreign language content with the wrong voice can be confusing to a screen reader user. - Identify the language for a document or its parts (University of Washington)

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Current research suggests that one element of good comprehension is sequencing ability (Gouldthorp, Katsipis & Mueller, 2017). Each of the exercises in this section requires the student to determine the order in which events occurred. This is achieved in several ways: - Identifying the event that occurred first. - Placing a number of sentences in a logical order to tell a story. - Deciding whether a statement concerning the order of an event occurring in a short passage is true or false. If students have difficulty determining the sequence of events in a story, it may be helpful to get them to retell the key events in the order of occurrence by asking: What happened first? What happened next? Then what? What happened last? It is also useful to draw their attention to key words in the text which signal order (e.g., first, after, then, finally, in the end, when, at the same time, before, during, as, following, since, while, next, etc.). Another strategy is to have students think about the story as a movie. If they were a movie director, turning the story into a movie, what would be the scenes they would set up and in what order? Gouldthorp, B., Katsipis, L., & Mueller, C. (2017). An investigation of the role of sequencing in children’s reading comprehension. Reading Research Quarterly. DOI:10.1002/rrq.186

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Fire burns as a reaction when matter changes form and is part of a chemical reaction that produces heat and light. In order for a fire to start, some form of fuel must be heated to its ignition temperature. After a fuel is heated to its burning point, part of it is decomposed and released as a volatile gas. This gas is known as smoke and contains hydrogen, carbon and oxygen. The remainder forms char, which is mostly carbon and ash and includes any other noncombustible elements. The next part of the burning process requires the volatile gases released to reach a certain temperature, which is about 500 degrees Fahrenheit for wood. Once this temperature has been reached, the molecules in the gas break down and the atoms combine with oxygen to form carbon dioxide, water, carbon monoxide, nitrogen and carbon. This chemical process causes flammable objects to burn. At the same time, the carbon from the char reacts with oxygen to form a much slower reaction. This particular reaction explains how charcoal in a grill can remain hot for long periods of time. A further side effect of these reactions is heat. The heat is what ultimately ends up sustaining a fire until the fuel has been completely burned up.

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Opposition to the flow of current is called resistance and the device or component used for this purpose is called resistor. Resistors restrict the flow of electric current, for example a resistor is placed in series with a light-emitting diode (LED) to limit the current passing through the LED. Connecting and soldering Resistors may be connected either way round. They are not damaged by heat when soldering. Resistor values - the resistor color code Resistance is measured in ohms, the symbol for ohm is an omega Ω 1 Ω is quite small so resistors values are often given in kΩ (Kilo Ohm's) and MΩ (Mega Ohm's). 1 kΩ = 1000 Ω 1 MΩ = 1000000 Ω Resistors values are normally shown using colored bands. Each color represents a number as shown in the table. Most resistors have 4 bands: |The Resistor Color Code| The first band gives the first digit. - The second band gives the second digit. - The third band indicates the number of zeros. - The fourth band is used to shows the tolerance (precision) of the resistor, this may be ignored for almost all circuits but further details are given below. This resistor has red (2), violet (7), yellow (4 zeros) and gold bands. So its value is 270000 Ω= 270 kΩ On circuit diagrams the Ω is usually omitted and the value is written 270K. Small value resistors (less than 10 ohm) The standard color code cannot show values of less than 10Ω. To show these small values two special colors are used for the third band: gold which means × 0.1 and silver which means × 0.01. The first and second bands represent the digits as normal. red, violet, gold bands represent 27 × 0.1 = 2.7 green, blue, silver bands represent 56 times 0.01 = 0.56 Ω Tolerance of resistors (fourth band of color code) The tolerance of a resistor is shown by the fourth band of the color code. Tolerance is the precision of the resistor and it is given as a percentage. For example a 390Ω resistor with a tolerance of ±10% will have a value within 10% of 390Ω, between 390 - 39 = 351Ω and 390 + 39 = 429Ω (39 is 10% of 390). A special color code is used for the fourth band tolerance: silver ±10%, gold ±5%, red ±2%, brown ±1%. If no fourth band is shown the tolerance is ±20%. Tolerance may be ignored for almost all circuits because precise resistor values are rarely required. Resistor values are often written on circuit diagrams using a code system which avoids using a decimal point because it is easy to miss the small dot. Instead the letters R, K and M are used in place of the decimal point. To read the code: replace the letter with a decimal point, then multiply the value by 1000 if the letter was K, or 1000000 if the letter was M. The letter R means multiply by 1. 560R means 560 Ω 2K7 means 2.7 kΩ= 2700 Ω 39K means 39 kΩ 1M0 means 1.0 MΩ = 1000 kΩ Calculate how much ohm resister will be required for 1 LED to plug with Identify at least 3 resisters ohms with the help of color Bands.

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Loose parts are items and materials that we can move, adapt, change and manipulate. Play with loose parts is not only fun, it also develops literacy skills as children use creativity, problem solving and language as they negotiate what an item will represent. The materials come with no specific set of directions, they can be used along with or combined with other materials. Children can turn them into whatever they desire. These objects invite conversations and interactions; they encourage collaboration and cooperation. Loose parts promote social competence because they support creativity and innovation. All of these are valued skills we need as adults. Examples of loose parts include stones, buttons, wooden cubes, twigs, leaves, pinecones, fabric, beads, balls, rope, sticks, shells and Q-tips. The list goes on. Children acquire their first math skills and numerical concepts when they manipulate small loose parts. Using blocks and bottle caps for sorting, classifying, combining and separating is math in action! Children learn one-to-one correspondence when they make connections among those loose parts. You will commonly hear them counting and arranging the parts in specific sequences, patterns and categories by color, type and number. Loose parts come with no instructions - rather they invite children to use their imaginations to build, invent, choose, collaborate, consider and more. With loose parts play, the possibilities are only limited by our imaginations. Who knows where loose parts play adventures will take us? It is an exciting mystery tour of fun and learning! Community Literacy Coordinator Columbia Basin Alliance for Literacy – Trail and Area

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This IP lesson will focus on layer two switches, which are almost exclusively Ethernet switches. We’ll also consider how they are used to implement virtual local area networks (VLANS). Figure 1: L2 Switch Figure 1 illustrates a notebook computer sending an Ethernet frame through a switch and on to a server. The first task is to understand how the switch knows the proper outgoing port. Within the switch is a filtering table that contains the hardware (MAC) addresses of all devices that are attached to the switch and the corresponding port to which the device is attached. So, when a frame arrives at the switch, the interface reads the destination MAC address and looks in the table for the proper outgoing port. It then relays the frame. If the frame arrives and contains an error, it will be dropped. Typically this fact is recorded for the purposes of network management. A striking advantage of using switches is that they seem to increase available network bandwidth. In our figure we have a 16 port switch. Let’s suppose each port operates at 1Gb/sec. Can the network operate only at 1 Gb/sec? The answer is no. It can actually pass a total of 8 Gb/sec of traffic. This is because there can be eight conversations passing through the switch at any given instant. The switch builds its address filtering table by observing the first few frames passing among devices. In our figure, the first frame from the notebook to the server will go out all ports. But, when the server responds, the switch will know that the notebook is connected to port 2 and the server is connected to port 13. Figure 2: VLANS VLANs create networks that aren’t physically separate but act as if they are. Suppose in Figure 2 we have devices connected to ports 1-4 and we want to be able to interchange frames. Suppose also that we want the remaining devices to connect to each other using ports 5-16. If we configure the switch to use ports 1-4 as VLAN1 and ports 5-16 as VLAN2, this will be recorded in our filtering table. Now devices connected to VLAN1 cannot interchange frames with devices in VLAN2. In order to allow interaction between the devices on separate VLANS, the switch must support VLAN routing. However, when it does this it is actually performing a layer three function and will depend upon device IP addresses. More specifically, the switch will be performing this function as if it was a router. Phil Hippensteel, PhD, is a regular contributor to AV Technology. He teaches at Penn State Harrisburg.

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Nuclear engineers traditionally use a protective covering – known as cladding – to seal the heavy metal fuel so that the radioactive byproducts of nuclear fission are retained in a controlled location. Cladding's main function is to keep the plant systems as free from contamination as possible. Cladding material selection is based on required operating temperature, neutron economy, and compatability with the coolant and other core materials. For natural uranium reactors, primary selection criteria is a low neutron absorption cross section. A material that absorbs more than its share of neutrons would prevent the reactor from being able to produce any power at all. The earliest natural uranium reactors – designed for solely for plutonium production – used aluminum cladding. Aluminum is a corrosion resistent metal with a very low neutron affinity, but its melting point is too low for use in a power reactor. The European reactor designers had a choice of Magnox, an alloy of magnesium oxide and aluminum or a magnesium zirconium alloy. There are few differences between the two materials. The British chose Magnox while the French chose MgZr. Both materials' melting point is high enough to enable useful steam production, but their limiting temperature is much lower than materials used in other types of power systems. This leads to low thermal efficiency and higher power costs. The name "Magnox" is widely used to refer to the early gas cooled reactors because it provides a simple way to uniquely identify the group. While the American submarine reactor designers had to be concerned about interactions between the fuel and hot water in case of a cladding failure, this was less of a concern for the French and British. As long as its temperature is kept below 1000 F, CO2 does not interact chemically with uranium metal. Efficient heat transfer was the primary consideration for the Europeans; because they were using a gaseous coolant and a cladding that was only capable of limited temperatures, they needed to choose a fuel material with high thermal conductivity. Uranium metal has a much higher thermal conductivity than uranium dioxide does. The use of metal, rather than metallic oxide, also improved the neutron economy and eased the task of recycling the fuel material to extract useful isotopes. Choosing metallic uranium had its price, however. Uranium metal is more susceptible to irradiation damage, and it undergoes significant dimensional changes at relatively modest temperatures. These characteristics put a low limit on the potential fuel burn-up and the potential efficiency of the system. The early Magnox fuel required replacement after only producing about 3500 MWdays/tonne of heavy metal. For comparison, modern light water reactor fuel is replaced after producing approximately 40,000 MWdays/tonne of heavy metal. The theoretical limit is about 1,000,000 MWdays/tonne of heavy metal. Magnox designers partially overcame this low fuel burn-up by designing the reactors to be refueled while producing electrical power. This capability improves operating economy by allowing the production facility to generate revenue during a larger portion of the year. The low fuel burn up, though a significant disadvantage for single purpose reactors producing only electrical power, actually improved the weapons material production ability of the Magnox reactors. Fuel elements with short active lives are better sources of bomb grade plutonium than those that have remained in a reactor long enough to produce significant quantities of Pu-240, an isotope that increases the difficulty of bomb construction. The ability to produce good bomb material was a strong selling point to the governments that provided the initial funding needed to build the Magnox reactors. Later, however, this capability, rather than being valued by the market, became a significant inhibitor to their commercial viability. Finned Fuel Elements The low heat capacity of gas coolants compared to liquid coolant like water or sodium encouraged heat transfer engineers to design finned fuel elements to increase the surface area and to enhance gas mixing. One can get a good idea of what finned heat exchangers look like by closely observing the design of car radiators or air conditioning coolers. While the fins improved the reactor performance, they increased the cost and complexity of fuel element manufacture compared to the simple tubes found in pressurized water reactors. Magnox fuel designers also kept trying out new fin patterns to enhance fuel performance, thus preventing standardization and mass production economies. The high cost of finned fuel elements became a factor in the market battle between American light water reactors and the British/French type of gas cooled reactors.

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(set-up will begin at 6:00, viewing at 6:30) -Everyone will need to provide a project board for their project (watch for sales or coupons at Hobby Lobby). Make sure it is visually appealing and has a catchy title! -Please remember to bring a tarp to put under your table if your project might be messy. And so sorry to my favorite teen boys, but no fire. We can’t afford to replace church buildings ;). Below is the Scientific method which you can outline on your board. Science fair projects are going to be different for different age groups, so just make it appropriate for your level. Preschoolers probably aren’t able to completely understand scientific method, but they can set out books on their topic, information they’ve collected, pictures, etc. Older kids can get more involved in the method. Scientific Method provides a framework in which scientists can analyze situations, explain things and answer questions. Steps of Scientific Method - Observation: allows the scientist to collect data - Once enough data has been collected, a hypothesis can be formed Hypothesis: an educated guess that attempts to explain a question - Once the hypothesis is formed, the scientist then collects much more data in an effort to test the hypothesis. If the data are found to be inconsistent with the hypothesis, the hypothesis might be discarded or modified until it is consistent with all the data that has been collected. - If a large amount of data is collected and the hypothesis is consistent with all the data, the hypothesis becomes a theory. Theory: a hypothesis that has been tested and is consistent with generations of data - If several generations of collected data are all consistent with the theory, it eventually attains the status of scientific law Science cannot prove anything. It is important to remember that the conclusions of science are always tentative. You can apply scientific method to show that there is evidence for your hypothesis. If your data confirms your hypothesis, it means that your hypothesis isscientifically reasonable. How Scientific Method Can Be Used in Your Mad Science Fair Project - Make Observations Take what is around you and start writing down observations. Write down everything-colors, timing, sounds, temperatures, light levels. Write down observations until a testable idea comes up. - Formulate a Hypothesis Pose a statement that can be used to predict the outcome of future observations. - Design an Experiment - Test the Hypothesis/Perform Your Experiment It is important to keep all data. Make notes when something exceptional occurs. Write down observations related to your experiment that aren’t directly related to the hypothesis. - Accept or Reject Your Hypothesis Conclusions are formed based on the analysis of the data. Does the data fit the hypothesis? Hypothesis Accepted: This does not guarantee that it is the correct hypothesis. This means that the result of your experiment support the hypothesis. Hypothesis Rejected: Go back to Step 2. More observations and data collection are needed. And here are a few examples of projects you could take off with. -How Do Germs Spread? -Observe/Detail Your Favorite Animal -How Does the Shell of an Egg Protect a Baby Chick? -What Colors Are Really Present In Leaves? -Why Do Leaves Change Colors in the Fall? -What Do Animals Do in the Winter? (Hibernation) -How Bubbles Work Homemade Ice Cream Vinegar, Baking Soda, Balloon -Polymers & Slime -Water & Ice -Does Wet Sand or Dry Sand Make The Best Sand Castels? -What Happens When Salt Water From The Ocean Evaporates? -How Does a Thermometer Work? Remember, the goal is to learn something new and to have fun! Can’t wait to see your great projects!

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This lesson can serve as introduction or a review to Shakespeare’s use of language, specifically how iambic pentameter and poetic verse is used to reveal character traits and plot elements. The overall goal is for students to feel and experience the language. Go beyond defining iambic pentameter by having students hear the rhythms of Shakespeare’s verse. By both speaking and scanning iambic pentameter during this lesson, students should be more prepared to analyze Shakespeare when they are studying and performing his work. Submitted by Mark Kuniya

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When we look for life elsewhere in the universe, we often focus on planets like our own: not too hot, not too cold ... warm enough for liquid water. But this model has one glaring problem: In the early days of our solar system, when life on Earth first developed, our sun only emitted about 70 percent of the energy it does today. That might not sound like a huge dissimilarity, but it's the difference between our planet being the beautiful blue marble we experience, and a frozen ice world. In other words, life shouldn't have been able to develop here — yet it somehow did. This problem is sometimes referred to as the "faint young sun paradox," and it has puzzled scientists for generations. There are theories, however. One leading theory posits an idea we're all familiar with today: a greenhouse effect. Perhaps the young Earth had a huge amount of atmospheric carbon dioxide, which would have trapped the faint sun's heat, and thus warmed the planet to a degree that made up for the lack of energy from the sun. The only problem with this theory is that it lacks evidence. In fact, geological evidence from ice cores and computer modeling suggest the opposite, that carbon dioxide levels were too low to make a big enough difference. Another theory suggests that Earth could have been kept warm due to a surplus of radioactive material, but calculations don't quite pan out here either. The young Earth would have needed much more radioactive material than it had. Some scientists have hypothesized that perhaps the moon could have warmed us, since in the planet's early days the moon would have been much closer to Earth and thus would have exhibited a stronger tidal influence. This would have had a warming effect, but again, calculations don't add up. It wouldn't have been enough to melt enough ice on a large scale. But now NASA scientists have a new theory, one that has held up to scrutiny so far, reports Quartz. Perhaps, they hypothesize, the sun was weaker but far more volatile than it is today. Volatility is the key; it essentially means that the sun may have once experienced more frequent coronal mass ejections (CMEs) — scorching eruptions that spew plasma out into the solar system. If CMEs were frequent enough, it might have poured enough energy into our atmosphere to make it warm enough for chemical reactions important for life to occur. This theory has a two-pronged advantage. First, it explains how liquid water might have formed on the young Earth, and it also provides the catalysis for chemical reactions that produce the molecules life needs to get started. “A rain of [these molecules] onto the surface would also provide fertilizer for a new biology,” explained Monica Grady of Open University. If this theory does hold up to scrutiny — a big "if" that will need to be investigated — it might finally offer a solution to the faint young sun paradox. It's also a theory that might help us to better understand how life began here on Earth, as well as how it might have gotten started elsewhere.

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Introduction To Prolog First Prolog Program What Is Prolog? Prolog is a declarative language. Programs in prolog are lists of facts and rules. When you execute a prolog program, you state a goal that you want to achieve. The program searches through all of the facts and rules attempting to reach this goal. Prolog programs are text files. This means that we can write them in a text editor like Notepad. Launch Notepad a file to your area as family tree.pl You will have to make sure that you select All Files in the save dialog. Type up the following facts for the family tree program. /* Family Tree Program */ /* facts */ The lines which begin and end with asterisks and forward slashes are comments - these are ignored when the program is run. All names must be in lower case - Prolog uses upper case for unknown information. All statements in Prolog end with a full stop. Your program will need some rules if it is going to be used to make decisions. Add the following lines to the bottom of your program. /* rules */ The first rule states that M is the mother of X if M is a parent of X and M is female. The father rule works in a similar way. Testing The Program Save your program. Launch Prolog. Click on File, Consult and select the program that you have saved. We will start by getting our program to find out who the parents of evelyn are. Type the following line in the Prolog window. In our statement, X stands for the information that we don't know. You should be given the answer X = dorothy. Press enter and type the following You should get the answer X = jack. Use the program to find out the following. - The father of liz - The mother of john - The father of grace Adding More Rules Return to your program and add the following rules. To get your program to use the new rules, first save your program. Now click on File and Reload Modified Files. Type in the following You should get the answer X = john. Now type in the following After the first answer, press the semi-colon key. You should get the second possible answer. Using The Anonymous Variable We can get our program to answer vaguer questions than the ones we have been putting. Suppose we want to find out who all the mothers in the system are. Type the following The underscore in Prolog is called the anonymous variable. This query should return all of the mothers in the system. Press the semi-colon after each answer. Creating A User Interface Expert systems can be made easier to use by creating an interface for the queries that you wish to run. Add the following to the bottom of your program. write('Whose mother do you want to find? '), write('The mother of '), write(Name), write(' is '), write(X), nl. To use this, type findMother. at the prompt. The program should help you with questions. Remember to place a full stop at the end of any line that you enter at the prompt. Extending The Program Using the information above, try to write some new rules for your program to find the brother, grandfather, grandmother of a person. Write interfaces for all standard queries in the system.

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When you write numbers in a base-10 numeral system, it is called decimal notation. Positional system involves a zero and symbols are used for ten values. It can represent a number irrespective of its size and the decimal separator is the indication of the start of a fractional part. The positions for each of the power of ten, hundreds, thousands are used by positional notation. Each position has a value of ten times more of the position on the right. The places to the left of the decimal point are ones, tens, hundreds and so on. The place exactly to the right of the decimal is called the tenths place. However, the place exactly to the left of the decimal point is ones place. Therefore, in decimals, the tens place is two places to the left of the decimal. The decimal is right at the middle of the ones place and the tenths place. Moreover, you should know that the values which are positioned to the right of the decimal point, boasts a “th†ending. Keep in Mind While Dealing with Decimals Addition and Subtraction - If you are dealing with decimal numbers, you need to keep in mind the rules for adding or subtracting whole numbers but you need to be careful of placing the decimal point in the same column as it is placed above. Moreover, you need to use 0 to provide same number of decimal places, whenever one number has more decimal places than the other number. Comparison - Comparing a decimal number can be little bit tricky as it does not go with the normal rule of number, which says that number with more digits is the larger one. In case of decimal numbers, first you need to consider the whole number portion first. If the number has more number of digits in the left part of the decimal then it is undoubtedly the larger number. However, in case of equal whole number, you need to assess the number towards the right of the decimal. Here, the number of digits doesn’t play any role. Assess them until you come to two different numbers and when you find that, the larger one among the two will make the larger number as a whole. Multiplication – In case of multiplications in decimals, you should not take into account the decimals at the beginning. Just proceed with the multiplication like any other multiplication. Once you are done with the multiplication, then comes the question of placing the decimal. All you need to do is to count all the places to the right of the decimal and count that number of places in the product and place the decimal. The counting should be from right to left. Division - If the dividend bears a decimal and the divisor doesn’t, then all you need to do is place the decimal in the quotient exactly above the decimal point in the dividend. However, if both the divisor and the dividend bear decimal then you need to count the number of places, you need to move the decimal point in order to make the divisor a whole number. You also need to move the decimal exactly the same number of places in case of the dividend and then while dividing you need to place the decimal in the quotient exactly above the new decimal point.

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Next: Debugging Up: Non-Programmers Tutorial For Python Previous: Count to 10 Contents n = input("Number? ") if n < 0: print "The absolute value of",n,"is",-n else: print "The absolute value of",n,"is",n Here is the output from the two times that I ran this program: Number? -34 The absolute value of -34 is 34 Number? 1 The absolute value of 1 is 1 So what does the computer do when when it sees this piece of code? First it prompts the user for a number with the statement n = input("Number? "). Next it reads the line if n < 0: If n is less than zero Python runs the line print "The absolute value of",n,"is",-n. Otherwise python runs the line print "The absolute value of",n,"is",n. More formally Python looks at whether the expression n < 0 is true or false. A if statement is followed by a block of statements that are run when the expression is true. Optionally after the if statement is a else statement. The else statement is run if the expression is false. There are several different tests that a expression can have. Here is a table of all of them: ||less than or equal to| ||greater than or equal to| ||another way to say not equal| Another feature of the if command is the elif statement. It stands for else if and means if the original if statement is false and then the elif part is true do that part. Here's a example: a = 0 while a < 10: a = a + 1 if a > 5: print a," > ",5 elif a <= 7: print a," <= ",7 else: print "Neither test was true" and the output: 1 <= 7 2 <= 7 3 <= 7 4 <= 7 5 <= 7 6 > 5 7 > 5 8 > 5 9 > 5 10 > 5 Notice how the elif a <= 7 is only tested when the if statement fail to be true. elif allows multiple tests to be done in a single if statement. #Plays the guessing game higher or lower # (originally written by Josh Cogliati, improved by Quique) #This should actually be something that is semi random like the # last digits of the time or something else, but that will have to # wait till a later chapter. (Extra Credit, modify it to be random # after the Modules chapter) number = 78 guess = 0 while guess != number : guess = input ("Guess a number: ") if guess > number : print "Too high" elif guess < number : print "Too low" print "Just right" Guess a number:100 Too high Guess a number:50 Too low Guess a number:75 Too low Guess a number:87 Too high Guess a number:81 Too high Guess a number:78 Just right #Asks for a number. #Prints if it is even or odd number = input("Tell me a number: ") if number % 2 == 0: print number,"is even." elif number % 2 == 1: print number,"is odd." else: print number,"is very strange." Tell me a number: 3 3 is odd. Tell me a number: 2 2 is even. Tell me a number: 3.14159 3.14159 is very strange. #keeps asking for numbers until 0 is entered. #Prints the average value. count = 0 sum = 0.0 number = 1 #set this to something that will not exit # the while loop immediatly. print "Enter 0 to exit the loop" while number != 0: number = input("Enter a number:") count = count + 1 sum = sum + number count = count - 1 #take off one for the last number print "The average was:",sum/count Enter 0 to exit the loop Enter a number:3 Enter a number:5 Enter a number:0 The average was: 4.0 Enter 0 to exit the loop Enter a number:1 Enter a number:4 Enter a number:3 Enter a number:0 The average was: 2.66666666667 #keeps asking for numbers until count have been entered. #Prints the average value. sum = 0.0 print "This program will take several numbers than average them" count = input("How many numbers would you like to sum:") current_count = 0 while current_count < count: current_count = current_count + 1 print "Number ",current_count number = input("Enter a number:") sum = sum + number print "The average was:",sum/count This program will take several numbers than average them How many numbers would you like to sum:2 Number 1 Enter a number:3 Number 2 Enter a number:5 The average was: 4.0 This program will take several numbers than average them How many numbers would you like to sum:3 Number 1 Enter a number:1 Number 2 Enter a number:4 Number 3 Enter a number:3 The average was: 2.66666666667 Modify the password guessing program to keep track of how many times the user has entered the password wrong. If it is more than 3 times, print ``That must have been complicated.'' Write a program that asks for two numbers. If the sum of the numbers is greater than 100, print ``That is big number''. Write a program that asks the user their name, if they enter your name say "That is a nice name", if they enter "John Cleese" or "Michael Palin", tell them how you feel about them ;), otherwise tell them "You have a nice name". Next: Debugging Up: Non-Programmers Tutorial For Python Previous: Count to 10 Contents Josh Cogliati email@example.com Wikibooks Version: Wikibooks Non-programmers Python Tutorial Contents

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