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Black Americans’ quest for official racial equality began the moment Reconstruction ended in the late 1870s. Even though Radical Republicans had attempted to aid blacks by passing the Civil Rights Act of 1866, the Ku Klux Klan Act, the Civil Rights Act of 1875, as well as the Fourteenth Amendment and Fifteenth Amendment, racist whites in the South ensured that blacks remained “in their place.” The black codes, for example, as well as literacy tests, poll taxes, and widespread violence kept blacks away from voting booths, while conservative Supreme Court decisions ruined any chances for social equality. The Compromise of 1877 effectively doomed southern blacks to a life of sharecropping and second-class citizenship. In 1896, in the landmark Plessy v. Ferguson decision, the conservative Supreme Court upheld the racist policy of segregation by legalizing “separate but equal” facilities for blacks and whites. In doing so, the court condemned blacks to more than a half century more of social inequality. Black leaders nonetheless continued to press for equal rights. For example, Booker T. Washington, president of the all-black Tuskegee Institute in Alabama, encouraged African Americans first to become self-sufficient economically before challenging whites on social issues. W. E. B. Du Bois, a Harvard-educated black historian and sociologist, however, ridiculed Washington’s beliefs and argued that blacks should fight for social and economic equality all at once. Du Bois also hoped that blacks would eventually develop a “black consciousness” and cherish their distinctive history and cultural attributes. In 1910, he also helped found the National Association for the Advancement of Colored People (NAACP) to challenge the Plessy decision in the courtroom. Between World War I and World War II, more than a million blacks traveled from the South to the North in search of jobs, in what became known as the Great Migration. The Harlem neighborhood of New York City quickly became the nation’s black cultural capital and housed one of the country’s largest African-American communities, of approximately 200,000 people. Even though most of Harlem’s residents were poor, during the 1920s, a small middle class emerged, consisting of poets, writers, and musicians. Artists and writers such as Langston Hughes and Zora Neale Hurston championed the “New Negro,” the African American who took pride in his or her cultural heritage. The flowering of black artistic and intellectual culture during this period became known as the Harlem Renaissance. Meanwhile, Marcus Garvey, a Jamaican immigrant and businessman, worked hard to promote black pride and nationalism. He founded the Universal Negro Improvement Association, which emphasized economic self-sufficiency as a means to overcome white dominance. He also encouraged blacks to leave the United States and resettle in Africa. Although most of Garvey’s business ventures failed and he was eventually deported back to Jamaica, his message influenced many future civil rights leaders. More than a million black men served in the Allied forces during World War II, mostly in segregated noncombat units. At home, black leaders continued to push for racial equality and campaigned for the “Double V”—victory both at home and abroad. In 1941, A. Philip Randolph, the president of the National Negro Congress, threatened to lead thousands of black protesters in a march on Washington to demand the passage of more civil rights legislation. President Franklin Delano Roosevelt, afraid that the march might disrupt the war effort, compromised by signing Executive Order 8802 to desegregate war factories and create the Fair Employment Practices Committee. As a result, more than 200,000 blacks were able to find top jobs in defense-related industries. After the war, President Harry S Truman created the President’s Committee on Civil Rights and desegregated the military with Executive Order 9981 . In 1954, after decades of legal work, Thurgood Marshall, the NAACP’s chief counsel, finally managed to overturn the “separate but equal” doctrine (established in Plessy v. Ferguson) in Brown v. Board of Education of Topeka, Kansas . Sympathetic Supreme Court chief justice Earl Warren convinced his fellow justices to declare unanimously that segregated public schools were inherently unequal. The Brown decision outraged conservative southern politicians in Congress, who protested it by drafting the Southern Manifesto. In 1957, Arkansas governor Orval Faubus chose to ignore a federal court order to desegregate the state’s public schools and used the National Guard to prevent nine black students from entering Central High School in Little Rock. Although President Dwight D. Eisenhower personally opposed the Brown decision, he sent federal troops to integrate the high school by force and uphold federal supremacy over the state. In 1955, the modern civil rights movement was effectively launched with the arrest of young seamstress Rosa Parks in Montgomery, Alabama. Police arrested Parks because she refused to give up her seat to a white man on a Montgomery city bus. After the arrest, blacks throughout the city joined together in a massive rally outside one of the city’s Baptist churches to hear the young preacher Martin Luther King Jr. speak out against segregation, Parks’s arrest, and the Jim Crow law she had violated. Blacks also organized the Montgomery bus boycott, boycotting city transportation for nearly a year before the Supreme Court finally struck down the city’s segregated bus seating as unconstitutional. In 1957, King formed the Southern Christian Leadership Conference (SCLC) to rally support from southern churches for the civil rights movement. Inspired by Indian political activist Mohandas Gandhi, King hoped the SCLC would lead a large-scale protest movement based on “love and nonviolence.” Although the SCLC failed to initiate mass protest, a new student group called the Student Nonviolent Coordinating Committee (SNCC) accomplished much. The SNCC was launched in 1960 after the highly successful student-led Greensboro sit-in in North Carolina and went on to coordinate peaceful student protests against segregation throughout the South. The students also helped the Congress of Racial Equality (CORE) organize Freedom Rides throughout the Deep South. In 1961, groups of both black and white Freedom Riders boarded interstate buses, hoping to provoke violence, get the attention of the federal government, and win the sympathy of more moderate whites. The plan worked: angry white mobs attacked Freedom Riders in Alabama so many times that several riders nearly died. Still, many of the students believed that the media attention they had received had been worth the price. The overwhelming public support from the North for Freedom Riders prompted Martin Luther King Jr. to launch more peaceful protests, hoping to anger die-hard segregationists. In 1963, King focused all of his energy on organizing a massive protest in the heavily segregated city of Birmingham, Alabama. Thousands of blacks participated in the rally, including several hundred local high school students who marched in their own “children’s crusade.” Birmingham’s commissioner, “Bull” Connor, cracked down on the protesters using clubs, vicious police dogs, and water cannons. King was arrested along with hundreds of others and used his time in jail to write his famous “Letter from Birmingham Jail” to explain the civil rights movement to critics. The violence during the Birmingham protest shocked northerners even more than the violence of the Freedom Rides and convinced President John F. Kennedy to risk his own political future and fully endorse the civil rights movement. Meanwhile, in 1963, King and the SCLC joined forces with CORE, the NAACP, and the SNCC in organizing the March on Washington in August. More than 200,000 blacks and whites participated in the march, one of the largest political rallies in American history. The highlight of the rally was King’s sermonic “I have a dream” speech. Kennedy was assassinated in November 1963, but the new president, Lyndon B. Johnson, honored his predecessor’s commitment to the civil rights movement. Johnson actually had opposed the movement while serving as Senate majority leader but changed his mind because he wanted to establish himself as the leader of a united Democratic Party. He therefore pressured Congress to pass the Civil Rights Act of 1964 , an even tougher bill than Kennedy had hoped would pass. The act outlawed discrimination and segregation based on race, nationality, or gender. The same year, the Twenty-Fourth Amendment to the U.S. Constitution was ratified, outlawing poll taxes as a prerequisite for voting in federal elections. Furthermore, SNCC activists traveled to Mississippi that summer on the Freedom Summer campaign to register more black voters, again hoping their actions would provoke segregationist whites. Violent opposition to the Freedom Summer campaign convinced Martin Luther King Jr. that more attention needed to be drawn to the fact that few southern blacks were actually able to exercise their right to vote. Springing into action, King traveled to the small town of Selma, Alabama, in 1965, to support a local protest against racial restrictions at the polls. There, he joined thousands of blacks peacefully trying to register to vote. Police, however, attacked the protesters on “Bloody Sunday,” killing several activists in the most violent crackdown yet. The same year, an outraged Lyndon B. Johnson and Congress responded by passing the Voting Rights Act to safeguard blacks’ right to vote. The act outlawed literacy tests and sent thousands of federal voting officials into the South to supervise black voter registration. However, a growing number of black activists had begun to oppose integration altogether by the mid-1960s. Malcolm X of the Nation of Islam was the most vocal critic of King’s nonviolent tactics. Instead, Malcolm X preached black self-sufficiency, just as Marcus Garvey had four decades earlier. He also advocated armed self-defense against white oppression, arguing that bloodshed was necessary for revolution. However, Malcolm X left the Nation of Islam after numerous scandals hit the organization, and he traveled to Mecca, Saudi Arabia, on a religious pilgrimage in 1964. In the course of his journey, he encountered Muslims of all nationalities who challenged his belief system and forced him to rethink his opinions regarding race relations. When Malcolm X returned to the United States, he joined forces with the SNCC in the nonviolent fight against segregation and racism. However, he was assassinated in early 1965. Despite Malcolm X’s untimely death, his original message of race separation (instead of integration) lived on and inspired many students in the SNCC, who also expressed dissatisfaction with the gains made through peaceful protests. Although the Civil Rights Act and Voting Rights Act were landmark laws for the civil rights movement, young activists such as Stokely Carmichael felt they had not done enough to correct centuries of inequality. In 1967, Carmichael argued in his book Black Power that blacks should take pride in their heritage and culture and should not have anything to do with whites in the United States or anywhere else. In fact, Carmichael even promoted one plan to split the United States into separate black and white countries. Frustrated activists in Oakland, California, responded to Stokely Carmichael’s “black power” theories and formed the Black Panther Party for Self-Defense. The Black Panthers, armed and clad in black, operated basic social services in the urban ghettos, patrolled the streets, and called for an armed revolution. Although the Black Panthers did provide valuable support to the community, their embrace of violence prompted a massive government crackdown on the group, leading to its dissolution in the late 1960s and early 1970s. Black revolutionaries such as Malcolm X, Stokely Carmichael, and the Black Panthers, along with the scores of race riots that rocked America between 1965 and 1970, frightened many white Americans and alienated many moderates who had supported peaceful protest. President Lyndon B. Johnson had also become suspicious of civil rights activists and ordered the FBI to begin investigations of Malcolm X, the Nation of Islam, and even Martin Luther King Jr. himself for their alleged ties to Communist organizations. Then, in 1968, a young white man named James Earl Ray shot and killed King as he addressed a crowd gathered in Memphis, Tennessee. King’s death, combined with the increasing amount of violence, effectively ended the civil rights movement of the 1950s and 1960s. Take a Study Break!

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In the “Connect Word Parts” worksheets, the student must draw a line to connect the "parts" to make a complete word. This file contains 8 worksheets. The following words are covered: a, and, away, big, blue, can, come, down, find, for, funny, go, help, here, I, in, is, it, jump, little, look, make, me, my, not, one, play, red, run, said, see, the, three, to, two, up, we, where, yellow, you Visual Perceptual Skills Addressed: Visual Analysis and Synthesis Visual Analysis and Synthesis is the ability to recognize how certain parts make a whole. In the “Connect Word Parts” worksheets, the student must identify which letter combinations fit together to form a word (see how the “pieces” form a “whole”). Figure Ground perception is the ability to screen out any irrelevant visual material when presented with a lot of visual information at one time (to locate the important stimulus without getting confused by the background or surrounding images). This skill is key for good attention and concentration. To complete the “Connect Word Parts” worksheets successfully, the student must focus on one “part” at a time within the busy field of all the surrounding “parts”. Visual Motor Integration Visual Motor Integration relates to the coordination of visual perceptual skills with body movement (the use of visual information to guide a motor task). For fine motor tasks, the eyes inform the arm and hand muscles where to go like "follow the leader”, so that motor output matches visual input. In the “Connect Word Parts” worksheets, the student's eyes must guide their hand to draw a line connecting the “parts” in a fluid and controlled manner. These worksheets form part of the Visual Perceptual Sight Words Builder 1 For more information please visit: www.visuallearningforlife.com

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Everything kids need to know about triangles—vocabulary, explanations and all. Beginning with the definition of a triangle and a breakdown of its parts—sides, angles, vertices—Adler quickly launches into a discussion of angles, even teaching kids how they are named, measured and classified. A clever activity instructs readers to cut out a triangle, any triangle. By tearing off the corners and lining them up so the vertices touch, kids can see that the angles of a triangle always sum 180 degrees. Vocabulary is printed in bold type and defined within the text, each new term building on the ones that have come before: “All three angles in ?ABC…are acute angles. ?ABC is an acute triangle.” In the primary-colored digital illustrations, a dark-skinned boy and a light-skinned girl are accompanied by a robot as they progress through the book, drawing and studying triangles. They accumulate materials to make another robot and then identify the angles and triangles that make up its body. Labels and diagrams make the learning easy, while the endpapers show several examples of each type of triangle presented. A final activity challenges readers to use their arms and hands to find and name angles—a turn of the page supplies labeled answers. With lots of layers of information, this is a book that can grow with kids; new information will be accessible with each repeat reading. (Math picture book. 6-10)

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The 19th Amendment to the U.S. Constitution, guaranteeing women the right to vote, is passed by Congress and sent to the states for ratification. The women’s suffrage movement was founded in the mid-19th century by women who had become politically active through their work in the abolitionist and temperance movements. In July 1848, 240 woman suffragists, including Elizabeth Cady Stanton and Lucretia Mott, met in Seneca Falls, New York, to assert the right of women to vote. Female enfranchisement was still largely opposed by most Americans, and the distraction of the North-South conflict and subsequent Civil War precluded further discussion. During the Reconstruction Era, the 15th Amendment was adopted, granting African American men the right to vote, but the Republican-dominated Congress failed to expand its progressive radicalism into the sphere of gender. In 1869, the National Woman Suffrage Association, led by Susan B. Anthony and Elizabeth Cady Stanton, was formed to push for an amendment to the U.S. Constitution. Another organization, the American Woman Suffrage Association, led by Lucy Stone, was organized in the same year to work through the state legislatures. In 1890, these two societies were united as the National American Woman Suffrage Association. That year, Wyoming became the first state to grant women the right to vote. By the beginning of the 20th century, the role of women in American society was changing drastically; women were working more, receiving a better education, bearing fewer children, and several states had authorized female suffrage. In 1913, the National Woman’s party organized the voting power of these enfranchised women to elect congressional representatives who supported woman suffrage, and by 1916 both the Democratic and Republican parties openly endorsed female enfranchisement. In 1919, the 19th Amendment, which stated that “the rights of citizens of the United States to vote shall not be denied or abridged by the United States or by any State on account of sex,” passed both houses of Congress and was sent to the states for ratification. On August 18, 1920, Tennessee became the 36th state to ratify the amendment, giving it the two-thirds majority of state ratification necessary to make it the law of the land. Eight days later, the 19th Amendment took effect.

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Atoms and Element Unit Essentials Lesson 1 of 13 Objective: SWBAT access a coherent, standards-based unit regarding atoms and elements. Great science units combine engaging investigations, opportunities for practice of science skills and strategies to frame all of that learning. This lesson provides resources and rationale for starting and ending a unit paired with some routines and procedures to help everything in between. Starting activities include vocabulary acquisition, essential questions, "pre-review" study guides and daily warm ups. End of unit activities include review strategies, assessment choices, assessment tools and rubrics. All of these resources support: Develop models to describe the atomic composition of simple molecules and extended structures (MS-PS1-1). Analyze and interpret data on the properties of substances before and after the substances interact to determine if a chemical reaction has occurred (MS-PS1-2). Starting a unit takes the perfect combination of backward planning, strategic development of routines and procedures, creative lesson ideas and enthusiasm. One way to make unit planning more efficient, is to find some best practice procedures and/or strategies that can be consistently used for every unit. These procedures and strategies act like a "frame" for each unit. The frame provides a consistent, repetitive structure within which students know what to expect. Students also practice and become more competent at the skills these procedures and strategies promote. Here are a few ideas for start of unit frames: 1) Vocabulary Acquisition - Familiarity with science vocabulary prior to in-depth investigation helps students develop a basis from which to start. As a routine at the start of each unit, students embark on a study of relevant vocabulary words. For a strategic lesson for vocabulary acquisition, check out: Learn-a-Word: Science Vocabulary Acquisition. Students can develop a vocabulary list or for a premade vocabulary list and extension ideas for this unit, visit this resource: Vocabulary Quiz - Atoms and Elements. A quick evaluation of student understanding may be appropriate too: Vocabulary Quiz - Atoms and Elements. For student-driven vocabulary projects, this Atoms and Elements Vocabulary Presentation - Student Extension and Atoms and Elements Vocabulary Picture Book are good examples. 2) Essential Questions - Essential questions frame a unit of study in terms of the the big, relevant, real-world issues or concepts. The purpose of essential questions is to engage students; promote critical thinking; and help students synthesize new experiences with prior knowledge. The essential question routine starts at the beginning of a unit with an introduction of the questions. Then, throughout the unit, each new learning experience needs to be explicitly connected back to these questions. Students don't always make connections on their own, so practicing this skill is paramount to the success of this strategy. For more on this topic and additional information about how and why to use essential questions, visit this related lesson: Force and Motion Essential Questions or Essential Questions: Building Student Engagement in Science Part 1 and Part 2. The essential questions for this unit are found here:Study Guide - Atoms and Elements. For student examples to peruse: Final Essential Questions - Atoms and Elements Student Example 1 and Final Essential Questions - Atoms and Elements Student Example 2. 3) "Pre-Review" Study Guides - Part of planning a great unit is using backward design to use standards to develop learning objectives - and then communicating those objectives to students, so they not only know what to expect, but for other reasons as well. The other reasons for providing a study guide prior to the unit are: 1) Students can use the guide to follow along as the unit unfolds; 2) Students can use the guide to self-assess their level of understanding and mastery; and 3) Students can prove mastery and use the other learning objectives to create self-directed study. The pre-review study guide is a routine that starts at the beginning of a unit with an introduction to the unit. As the unit progresses, students can check off learning objectives or keep a record of which investigations helped them master the learning objectives. At the close of a unit, students can use the guide for preparation for a final evaluation of learning. The study guide for this unit is provided here: Study Guide - Atoms and Elements 4) Daily Warm Ups - Daily warm ups, "do it nows" or "bell activities" serve the purpose of engaging students in the daily learning, focusing students for scientific study and to practice skills or learn concepts. This strategy can also serve the purpose of acting as a mini-lesson. For more on why I use this strategy, watch this: As discussed in the video, this resource: Essential Question and Warm Up Organizer - Atoms and Elements is helpful for students to use as a graphic organizer to keep their warm ups organized. An example of student warm ups for this unit can be viewed here: Warm Up - Atoms and Elements Student Example. An exit strategy for a unit is another optimal place for using procedures and strategies that can be consistently used for every unit. These procedures and strategies complete the "frame" for each unit that provides the consistent structure within which students know what to expect. Here are a few ideas for end of unit to complete the frame: 1) Assessment Choices - Backwards design suggests that assessment tools be designed prior to implementation of the unit of instruction. When approaching the end of the unit, it is time to ask students how they would like to be assessed. Just as differentiation occurs during instruction, a powerful strategy is to offer students choices in how they would like to be assessed. This handout: Assessment Choices Handout - Atoms and Elements, can be modified for any unit and additional rationale about this strategy occurs in this related lesson: Forces and Motion: Assessment Choices. 2) Review Strategies - Middle school students need instruction around how to assess themselves in terms of what they know and don't know...and then to make choices for how to study for an assessment. Providing time and structure for review activities is an important part of teaching students effective self-assessment and studying skills. One strategy that meets this need is the provision of a review checklist: Assessment Review Checklist - Atoms and Elements. A checklist like this one helps students organize their time and tasks during the review process. Additional strategies include setting up review stations during which students choose which activities would be most beneficial: Review Stations - Atoms and Elements. During this time, direct instruction with individual or groups of students can occur for those students who need additional support. A two-column review notes process: Review Notes - Atoms and Elements and Review Notes Answer Key - Atoms and Elements is another effective strategy. For more on this strategy, view this video: 3) Assessment Tools and Rubrics - Students have chosen the type of assessment they would like to take and prepared for it...When it is finally time for students to assess their understanding, they use the Assessment - Atoms and Elements or Science Portfolio - Atoms and Elements or Experimental Design Plan Blank, Experimental Design Plan Unguided or Experimental Design Plan depending on their assessment choice. To give students feedback on their work: Atoms and Elements Assessment Student Work, use these rubrics: Assessment Rubric - Atoms and Elements, Science Portfolio Rubric or the Complete Experimental Design Rubric. After students complete their assessments and feedback from the teacher is given, it is important for students to analyze how they performed. This lesson: Forces and Motion Assessment Review offers an alternative way for students to take charge of this process leading to reassessment if needed: Assessment Retake - Atoms and Elements. Teacher Note: For help developing an online science notebook where students can post their learning (like essential question responses, portfolios or experimental designs, this lesson is for you: Digital Science Notebook.

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Teacher's Guide to Studying Shakespeareby Arthea Reed, Ph.D. Please Note: this material was created for use in a classroom, but can be easily modified for homeschooling use. Before Reading the Play Most of us who love Shakespeare and Shakespearean drama are familiar with his plots, his characters, the historical background of each play, the Elizabethan theater, his dramatic conceits….It can be said that the better one is acquainted with Shakespeare’s plays, the more likely one is to enjoy them. Before asking students to delve into Shakespeare, it is important to help them gain the knowledge they need to enjoy the plays. (Note: The "Prefatory Remarks," "Introduction" and "Suggested References" in each Signet Classic Shakespeare are invaluable aids in the delving process.) - Assign each student to an investigative group: Shakespeare the man, Shakespeare the playwright, Shakespeare’s theater, Shakespeare’s England, the historical background of the play, the setting of the play. After the groups have completed their research, have them present the results. - Shakespeare’s plays can be divided broadly into comedies and tragedies. Since the tragedies frequently have comic elements and the comedies tragic, divide the class into two groups, one to investigate Elizabethan tragedy, the other to investigate Elizabethan comedy. Discuss the groups’ findings; list elements on chart paper for future reference. - Discuss the organization and dramatic techniques of Shakespearean drama: five acts divided into scenes; rising action, climax and falling action, chorus, prologue, soliloquy, asides, blank verse, use of mistaken identity, characters as foils, multiple meanings of words… - List characters on chart paper or the board (a list of characters is found at the beginning of each Signet Classic edition). Briefly discuss each, placing him/her within the context of the play (historic; social; comic or tragic; foil…). Discuss the character each student might like to portray. - Examine the vocabulary. Have students glance through the footnotes in the Signet Classic edition and identify unfamiliar words. Make a list of vocabulary by scene and act. Have each student look up at least one work to determine its definition and derivation. Pronounce the word, its definition and derivation. - Tell the story to the class. Is you are a good storyteller, here’s your chance to shine. Shakespeare’s tales are wonderful to tell. Be sure to help students recall his organizational and dramatic techniques.

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Flash cards are a classic teaching strategy. According to Brown et. al. (1983), flash cards can be in the form of photographs, drawings, or pictures cut from magazine, and newspapers. For a language instruction, drawings or pictures are not necessarily the work of art. The picture or drawing will be effective if they are used in the flash card. The picture in the flash card should be big enough, interesting, and clear for students to see. If the pictures are not big enough, not interesting, and not clear, the students will get confused to describe the pictures. The pictures can make students’ imagination deviate from what they are expected to produce. To avoid this, a teacher must follow the above criteria. In addition to a learning experience, Rice & Nash (2010) state that flash cards make a good self-assessment tool for students. One way to use flash cards in teaching narrative text is through Class-Wide Peer Tutoring (Westwood, 2010). Appropriate target words are selected by the teacher, usually based on a current theme, or an individual needs of the students. Each student works with a compatible partner for 10 minutes, they each take turns to act as “tutor” to help the other student master the word for the day. The first step is for each student to print his or her own target words on a flash card. The tutor then takes the tutee through some sequences: (1) The tutor holds up flash cards and says, “Look at this word. Say the word.”; (2) Close your eyes. Picture one of your classmates in your mind.”; (3) Now, open your eyes and check the person you have just think of; (4) write down the word on your paper; (5) The tutor then checks the written response and corrects any errors; (6) If there is no error, move to the next target word. If an error has been made, go back and repeat steps 1 to 4 again until correct; and (7) In a classroom situation, the teacher can move around to monitor students’ performance and give feedback. The other way of using flash cards is to use online system (Rice & Nash, 2010). A teacher can use a lesson, as if it is an online deck of flash cards. One advantage of using an online system is that log files tell the teacher if a student completed the flash card activity, and how well the student did. In a flash card lesson, every page will be a question page. In a lesson, a question page can have any content that the teacher can put on a normal web page. So, each page in the teacher’s flash card lesson can consist of a fully-featured web page, with a question at the bottom and some text-only feedback for each answer. When setting the jumps for each answer on the question page (on the card), make sure that a correct answer takes the student to the next page and an incorrect answer keeps them on the same page. Again, this duplicates our physical experiences with flash cards. When we get the correct answer, we move on to the next card. When we get the wrong answer, we try again until we have got right. A teacher can use a slide show setting to display the lesson in separate window, and make that window the size of a flash card. This can help create the effect of a deck of cards. Brown, J. W. Lewis, R. B. And Harcleroad, F.F. 1983. Audio Visual Instruction. New York: McGraw Hill. Rice, W. & Nash, S. S. 2010. Moodle 1.9 Teaching Techniques. Birmingham: PACKT Publishing. Westwood, P. 2010. Spelling: Approaches to Teaching and Assessment. Victoria: Acer Press.

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All Algebra II Resources Example Question #153 : Imaginary Numbers are real numbers. For two imaginary numbers to be equal to each other, their imaginary parts must be equal. Therefore, we set, and solve for in: Example Question #154 : Imaginary Numbers If and are real numbers, and , what is if ? To solve for , we must first solve the equation with the complex number for and . We therefore need to match up the real portion of the compex number with the real portions of the expression, and the imaginary portion of the complex number with the imaginary portion of the expression. We therefore obtain: We can use substitution by noticing the first equation can be rewritten as and substituting it into the second equation. We can therefore solve for : With this value, we can solve for : Since we now have and , we can solve for : Our final answer is therefore Example Question #155 : Imaginary Numbers Solve for if . Go about this problem just like any other algebra problem by following your order of operations. We will first evaluate what is inside the parentheses: . At this point, we need to know the properties of which are as follows: Therefore, and the original expression becomes Example Question #156 : Imaginary Numbers Evaluate and simplify . None of the other answers. The first step is to evaluate the expression. By FOILing the expression, we get: Now we need to simplify any terms that we can by using the properties of Therefore, the expression becomes Example Question #157 : Imaginary Numbers Solve for : In order to solve this problem, we need to first simplify our equation. The first thing we should do is distribute the square, which gives us Now is actually just . Therefore, this becomes Now all we need to do is solve for in the equation: which gives us Finally, we get and therefore, our solution is Example Question #4 : Imaginary Numbers & Complex Functions Solve for and : So the powers of are cyclic. This means that when we try to figure out the value of an exponent of , we can ignore all the powers that are multiples of because they end up multiplying the end result by , and therefore do nothing. This means that Now, remembering the relationships of the exponents of , we can simplify this to: Because the elements on the left and right have to correspond (no mixing and matching!), we get the relationships: No matter how you solve it, you get the values , . Example Question #158 : Imaginary Numbers All real numbers Subtract from both side: Which is never true, so there is no solution.

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Lesson 7 of 12 Objective: SWBAT differentiate between active and passive voices and use active voice to improve sentence structure. As a class, we quickly reviewed the difference between Active and Passive Voice using the Active/Passive Voice Power Point found in the Resources. As a class, we completed the first three examples together. Then, the class worked on the next 7 examples independently. We corrected them and discussed how the voice was identified. Students then completed the end of the worksheet independently and again we reviewed this in class. On the back of the worksheet, I printed a copy of a local news article. We discussed how news reporters should be writing in the active voice, making the writing more exciting with action verbs vs “be” verbs. With a partner, students highlighted verbs in the article and labeled whether it was active or passive voice. We shared as a class, noting that most of the article was written in active voice. A discussion of how it would change if written in the passive voice occurred.

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Using Standard Algorithms for Number Operations This lesson unit is intended to help students to make sense of standard algorithms for addition, subtraction, multiplication, and division of positive integers. In particular it should assist them in the following areas: - Improving conceptual understanding of why and how the algorithms work. - Developing procedural fluency in carrying out the algorithms. - Becoming more able to spot unreasonably sized answers and to debug errors in procedures. This lesson is structured in the following way: - Before the lesson, students work individually on an assessment task, Getting it Wrong, designed to reveal their current understanding and difficulties. You review their solutions and create questions for students to answer in order to improve their work. - The main lesson begins with a whole-class introduction, in which students critique systematic errors in standard algorithms. Students try to explain why what is being done does not work. - Then students work in pairs or threes on a collaborative task to find errors in some sample student work. They are encouraged to go beyond ‘correcting’ the answers to conjecturing why the student might have made the error and explaining why the method used does not (always) work. - In a whole-class discussion, students describe what they have learned from the task. - Finally, students receive your comments on the assessment task and use these to attempt a similar task, approaching it with insights that they have gained from the lesson. - Each student will need a copy of the assessment tasks Getting it Wrong and Getting it Wrong (revisited), a mini-whiteboard, pen, and eraser. - Each small group of students will need two cards from either Card Set (1) or Card Set (2) (already cut up) and some blank paper to work on. 20 minutes before the lesson, an 85-minute lesson (or two shorter lessons), and 20 minutes in a follow-up lesson. Timings given are approximate and will depend on the needs of your class. This lesson involves a range of mathematical practices from the standards, with emphasis on: - MP1: Make sense of problems and persevere in solving them - MP2: Reason abstractly and quantitatively - MP3: Construct viable arguments and critique the reasoning of others - MP6: Attend to precision - MP7: Look for and make use of structure - MP8: Look for and express regularity in repeated reasoning Mathematical Content Standards This lesson asks students to select and apply mathematical content from across the grades, including the content standards:

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All ACT Math Resources Example Question #1 : Negative Numbers What is 1 + (–1) – (–3) + 4 ? You simplify the expression to be 1 – 1 + 3 + 4 = 7 Example Question #2 : Negative Numbers Solve the following equation for : To begin, we need to recall how to subtract negative numbers. Remember, when subtracting a negative number, the two negatives cancel out, creating a positive. We can combine like terms on the left to get: Then, we can subtract from both sides in order to get by itself: In this case, we are subtracting from a negative number, which is just like adding two negative numbers, or subtracting from a positive number. The result will be more negative, because we will be moving further to the left on the number line. Example Question #1 : Describe Situations In Which Opposite Quantities Combine To Make 0: Ccss.Math.Content.7.Ns.A.1a Compute the following: Convert all the double signs to a single sign before solving. Remember, two minus (negative) signs combine to form a plus (positive) sign, and a plus (positive) sign and a minus (negative) sign combine to form a minus (negative) sign.

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Structural Biochemistry/Chemical Bonding/Covalent bonds Covalent bonds are chemical bonds that are formed by sharing valence electrons between adjacent atoms. This type of bonding is mostly seen in interactions of non-metals. Covalent bonds allow elements the ability to form multiple bonds with other molecules and atoms - a fundamental necessity for the creation of macromolecules. In the covalent bond, as the distance between the nuclei decreases, each nucleus starts to attract the other atom's electron, which lowers the potential energy of the system. Anyway, when the attraction increases, the repulsions between the nuclei and between the electrons increase as well. In covalent bonding, each atom achieves a full outer (valence) level of electrons. Each atom in a covalent bond counts the shared electrons as belonging entirely to itself. Most covalent substances have low electrical conductivity because electrons are localized and ions are absent. Overall, the atoms in a covalent bond vibrate, and the energy of these vibrations can be studied with the IR spectroscopy. A general rule to follow when looking at covalent bonding is the octet rule, also known as the noble gas configuration. An atom participating in covalent bonding must (with few exceptions) follow the octet rule, which states that an atom must have eight electrons around it. These electrons can be shared or unshared. The two atoms do not need to share their electrons equally; an electron pair can be donated from one atom instead of each atom donating one electron. A periodic table can be used to determine the number of valence electrons an atom. The general rule is that all atoms will be stable if they can have eight electrons around them. Therefore different atoms can share their unpaired electrons with other atoms with unpaired electrons to gain an octet. There are quite a few exceptions to this rule. Two very important ones are Hydrogen (H) and Helium (He). These atoms do not have octets and only need a total of two electrons to be stable. This is because hydrogen and helium only contain a 1s electron shell, which can only hold two electrons. Other exceptions occur when the total number of electrons in a molecule or between two molecules is an odd number. These molecules tend to be very reactive. Also, atoms past the second row on the periodic table can have more than eight electrons surrounding them. For example, in phosphorus pentafluoride (PF5) the phosphorus is bonded to 10 electrons, and in sulfur hexafluoride (SF6) the sulfur atom is bonded to 12 electrons. Molecules can also be electron deficient, meaning there are not enough available electrons to complete full octets around all the atoms in the molecule. An example of an electron deficient molecule is boron trichloride (BCl3). In this molecule, the boron atom is only bonded to three electron pairs, while the chlorides are surrounded by full octets. Types of Covalent Bonds Multiple covalent bonds can be formed between atoms, which are stronger than single bonds and have higher bond energy and shorter bond lengths. The bond order is used to determine the number of pairs of electrons in a covalent bond. When a molecule has double and single covalent bonds, it can have different chemical forms of equal energy as resonance structures, which has more stability and the bond is the average of the double and single covalent bond. The characteristics of a covalent bond can also be effected by the two atoms it joins. Single bonds are one of the weaker types of covalent bonds. Single covalent bonds are also called sigma bonds. These are made when only two electrons are shared. This leads to an overlap of the orbitals and a merging of the electron density clouds. Single bonds tend to be very flexible allowing atoms to rotate around the bond. An example of a single bond is a carbon-carbon (C-C) covalent bond has a bond length of 1.54 A and bond energy of 356 kJ/mol. Note that the properties of a single bond depends not only on the two atoms that is bonds but also on the atoms surrounding those atoms. Sigma bonds have no nodal planes. Some covalent single bonds will also have double bonds properties, which are shorter, rigid and non-rotated. One example is peptide bond in proteins which connect each amino acid together to form polypeptide. The peptide-bond is 1.32 A which is shorter than 1.54 A (C-C). The energy that needs to break the peptide bond is much higher than the single bond and this non-rotated single bond contributes the planar property in the polypeptide chain, which also makes the peptide bond more stable than the normal single bond. The double bond properties are contributed by the resonance structure of the pepetide bond. Double bonds occur when a covalent bond consists of four shared electrons. A double covalent bond contains a sigma bond and a pi bond. Pi-bonds apply to the overlapping p-orbitals. The orbitals can only overlap in a side-by-side arrangement leading to one nodal plane on the internuclear axis. A single covalent bond only contains a sigma bond. Double bonds tend to be shorter than their single bond equivalents and stronger. Double bonds also create electron density around the bond. Unlike single bonds, double bonds are not flexible and the two adjoining atoms cannot rotate about the bond. A triple covalent bond contains one sigma bond and two pi bonds where six electrons are being shared. These bonds are stronger than double bonds and shorter. They are more rigid than double bonds and have a larger electron density. The most common triple bonds are on carbons like C2H2. The skeletal form to draw a triple bond is three straight lines connecting the two atoms. Polar Covalent Bonds Covalent bonds can be polar or non-polar depending on the electro-negativity value of the atoms bonded together. If there is a very large difference between the two atoms' electro-negativity values, a polar covalent bond is formed. The atoms do not need to posses the same electro-negativity values, or be of the same element, but they need to be relatively close in their values. If the electro-negativity values are closer, the co-valency between the atoms will be stronger. An exception to this rule is when a molecule possesses symmetry. When the overall dipole moment is zero, such as linear molecule of CO2, the molecule is consider non-polar. The more electronegative atom will attract the electrons, making itself have a partial negative charge and giving the other atom a partial positive charge. These partial negative and positive charges are what account for the dipole-dipole, dipole-induce dipole, and induced dipole-induced dipole interaction. This attraction-to-repulsion stability is what gives the covalent bonds stability. In addition to the electro-negativity differences between atoms, covalent bonding also depends on the angles of adjacent atoms relative to each other. Typical accepted values for determination of type of bonds: Difference in electronegativity - X < 0.5 - Non-polar covalent bond Difference in electronegativity - 0.5 ≤ X ≤ 1.9 - Polar covalent bond Difference in electronegativity - 1.9 < X - Ionic bond Specific Types Of Covalent Bonds Disulfide Bonds In Chemical interactions, certain compounds can react to create a disulfide bond, which is a type of covalent bond that is usually derived by the coupling of two thiols (-S-H). These interactions can also be called SS-bonds or disulfide bridges, with the connectivity of these interactions mainly being R-S-S-R . Role in Protein Folding Disulfide bonds can play a vital role in the tertiary structure of proteins in the effect they have on protein folding and stability. These disulfide bonds between proteins usually are formed between the thiol groups of cysteine residues. The other amino acid group in which sulfur appears is methionine, which cannot form disulfide bonds. Disulfide bonds help to stabilize the tertiary structure of a protein molecule in several ways, for example, The disulfide bonds destabilize the unfolded form of a protein by lowering its overall entropy, or state or chaos. Also, when the disulfide bonds link two segments of the protein chain, this increases the effective local concentration of protein residues and lowers the effects of water in a that specific region. Since water molecules are known to attack amide-amide bonds, lowering the effects of water in these disulfide bond- regions helps to stabilize a protein. Covalent Bond: Bond Length and Bond Energy The bond energy (BE) is the energy required for the attraction or breakage between the atoms. Since it is the energy needed to break the attraction between the atoms, the bond energy is endothermic and positive. However, the energy required for the formation of the bond is exothermic and a negative value. The bond length is the distance between the nuclei of two covalent bonded atoms. It can be calculated based on the total radii of the bonded atoms. As a result, the bond length increases when the covalent radius increases. And the shorter the bond length, the higher bond energy will be needed to break the attraction between the atoms because shorter distance between the atoms means the bond will be stronger and harder to break. On the other hand, the longer the bond length is, the lower bond energy is needed to break a weaker bond. One can use bond energy to determine the ΔHrxn. In a reaction, when two atoms react with each other to form the product of different atoms, there are two types of bond energy. One is the energy required for the reactant to be broken and the other one is the energy required for products to be formed. As a result, the difference between the two bond energy is the enthalpy or the work of the reaction. ΔH0rxn= ΔHreactant bonds broken + ΔHproduct bonds formed - Organic Chemistry by Vollhardt and Shore - Berg, Jeremy; Tymoczko, John; Stryer, Lubert. Biochemistry, 6th edition. W.H. Freeman and Company. 2007. (7) - Silberberg, Martin S.(2010). Principles of General Chemistry (2nd Edition).McGraw Hill Publishing Company. ISBN978-0-07-351108-05 Silberberg, Martin S. Chemistry "The Molecular Nature of Matter and Change." Fifth Edition.

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This lesson teaches students the difference between accept and except. Examples are included with speech bubbles to show students how to think through that example. This lesson will help students reading comprehension as well as their writing conventions and word choice. The slides include practice opportunities, interactive matching, application to reading, and independent practice with constructing sentences using the correct form of either except or accept. This is also a great resource to use with English Language Learners.

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To repeat lines of code, you can use a function. A function has a unique distinct name in the program. Once you call a function it will execute one or more lines of codes, which we will call a code block. For example, we could have the Pythagoras function: In case your math is a little rusty, a^2 + b^2 = c^2. Thus, c = sqrt( a^2 + b^2). In code we could write that as: import math def pythagoras(a,b): value = math.sqrt(a *a + b*b) print(value) pythagoras(3,3) We call the function with parameters a=3 and b =3 on the last line. A function can be called several times with varying parameters. There is no limit to the number of function calls. The def keyword tells Python we define a function. Always use four spaces to indent the code block, using another number of spaces will throw a syntax error. It is also possible to store the output of a function in a variable. To do so, we use the keyword return. import math def pythagoras(a,b): value = math.sqrt(a*a + b*b) return value result = pythagoras(3,3) print(result) The function pythagoras is called with a=3 and b=3. The program execution continues in the function pythagoras. The output of math.sqrt(a*a + b*b) is stored in the function variable value. This is returned and the output is stored in the variable result. Finally, we print variable result to the screen.

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Students learn that a tree diagram shows all the possible outcomes of a situation. For example, a tree diagram can be used to show all the possible outcomes of choosing a small, medium, large, or extra large t-shirt in red or blue. Note that the first level of the tree would be the 4 different sizes, and the second level of the tree would be the 2 different colors for each size, so there are 8 possible outcomes. Students also learn the Counting Principle, which states that when one item is selected from each of two or more sets, the total number of possible outcomes is equal to the product of the number of items in each set. For example, in the t-shirt problem above, the two sets are size and color, and since there are 4 possible sizes and 2 possible colors, the total number of possible outcomes is 4 times 2, or 8.

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The idea of countable and uncountable nouns can be a difficult concept for students to grasp. Once they have understood the concept, it can take a long time to master and use correctly when speaking and writing. Visual examples are useful for helping your students understand the distinction. Try to take some food items into class. Show your students the items and as a whole class help them classify the items. They'll soon see the difference between coffee and carrot, for example. You can then explain or elicit the difference between mass (uncountable) and unit (countable). If you think your students are up to it, you can show the distinction between a cucumber and cucumber (as chopped up for a salad). Similar examples include: tea / teabags and sugar / sugar cubes. You can then draw 5 or 6 vertical lines on the board to represent units or countable items and a scribbled mass or criss cross of lines to represent mass or uncountable items. Students then organise the food items you have just studied into the categories. They can continue in pairs with pictures of other items or a list that you give them. Explain the use of singular or plural verbs with countable and uncountable items. Depending on their level and the amount of challenge you think they are ready for, they can make sentences using a picture you give them and the following structures: There's some ________ on the table There isn't any ________ on the table There are 5 ________ on the table There aren't any ________ on the table Are there any ________ on the table? Yes, there are / No, there aren't. Is there any ________ on the table? Yes, there is / No, there isn't. How much ________ is there? There's a lot / there isn't much. How many ________ are there? There are a lot / there aren't many. Try to incorporate both written and spoken work and follow up with more work in the next class.

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Exercise 31: Making Decisions In the first half of this book you mostly just printed out things called functions, but everything was basically in a straight line. Your scripts ran starting at the top and went to the bottom where they ended. If you made a function you could run that function later, but it still didn't have the kind of branching you need to really make decisions. Now that you have if, else, and elif you can start to make scripts that decide things. In the last script you wrote out a simple set of tests asking some questions. In this script you will ask the user questions and make decisions based on their answers. Write this script, and then play with it quite a lot to figure it out. A key point here is that you are now putting the if-statements inside if-statements as code that can run. This is very powerful and can be used to create "nested" decisions, where one branch leads to another and another. Make sure you understand this concept of if-statements inside if-statements. In fact, do the Study Drills to really nail it. What You Should See Here is me playing this little adventure game. I do not do so well. - Make new parts of the game and change what decisions people can make. Expand the game out as much as you can before it gets ridiculous. - Write a completely new game. Maybe you don't like this one, so make your own. This is your computer, do what you want. Common Student Questions - Can you replace elif with a sequence of if-else combinations? - You can in some situations, but it depends on how each if/else is written. It also means that Python will check every if-else combination, rather than just the first false ones like it would with if-elif-else. Try to make some of these to figure out the differences. - How do I tell if a number is between a range of numbers? - You have two options: Use 0 < x < 10 or 1 <= x < 10, which is classic notation, or use x in range(1, 10). - What if I wanted more options in the if-elif-else blocks? - Add more elif blocks for each possible choice.

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gcsescience.com 5 gcsescience.com Rates of Reaction How can the Rate of the Reaction Sodium Thiosulfate and dilute Hydrochloric Acid be Measured? HCl + sodium thiosulfate sodium chloride + sulfur dioxide + sulfur + water. 2HCl(aq) + Na2S2O3(aq) 2NaCl(aq) + SO2(g) + S(s) + H2O(l) The rate of this can be measured by looking at the rate at which the product solid sulfur (S(s)) is formed. The solid sulfur makes the colourless solution go cloudy. This reaction is usually carried out in a flask placed on a piece of white paper. The white paper has a black cross on it. At the beginning of the reaction, the cross can easily be seen through the solution in the flask. As the solution in the flask becomes more and more cloudy, the cross gets harder to see. You can measure the time from the start of the reaction until the cross can no longer be seen. This is a way of measuring the rate of formation of sulfur. The reaction between magnesium metal and a dilute can be followed in a similar way noting the time taken for the bubbles of hydrogen gas to stop forming or for the magnesium metal to disappear. See also how the rate of this reaction is affected by increasing the concentration of the solution. Links Catalysts and Energy Enzymes Revision Questions gcsescience.com The Periodic Table Index Reaction Rate Quiz gcsescience.com Home GCSE Chemistry GCSE Physics Copyright © 2015 gcsescience.com. All Rights Reserved.

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Pronouns are words that take the place of nouns. At their first introduction, they seem easy enough to master for most elementary students. However, at times there can be some complex issues where pronoun usage can get tricky. Spending a little extra time focusing on these issues in elementary school can help your students master the pronoun rules. Pronoun Picture Labels Core curriculum objectives require students to use personal, possessive and indefinite pronouns beginning in first grade. This activity using body movement reinforces cognitive learning in young students. Keep a large supply of pictures cut from magazines. Give each child a piece of cardstock on which you have written one of the following pronouns: he, she, it, his, hers, her, she, he, they, them. Tape the cardstock pronouns on each child’s chest. Hold up one of the magazine pictures from your supply, telling students to look for possible antecedents. Students whose pronoun can take the place of one of the antecedents in the picture should stand up. For instance, if you hold up a picture of a girl fishing with her father, students labeled “he,” “she,” “him,” “her,” “hers,” “his,” “they” and “them” could all stand. Alternatively, hand pictures out to students and have them write complete sentences about the pictures using no pronouns. Have them switch papers with a classmate to rewrite the sentences using pronouns. Pronoun Choice Buzz Game Create several strips with sentences that contain pronouns. Use grade-appropriate vocabulary and complexity. However, when you write the pronoun, give two choices, such as “One of the students forgot (their / his or her) lunch. Divide the class into two teams. Set up a table at the front of the room. On each side of the table, place a buzzer or a bell. Call one player from each team to the front of the room to stand in front of each buzzer. Reveal the sentence strip and have the students ring the buzzer as soon as they think they know which pronoun is correct. Call on the student who rang the buzzer first. If he or she answers correctly, that team wins a point. Play until all students have had a turn at the buzzer. Identifying Pronouns in Context Students in all grades will benefit from this activity. Using grade-level readers, tell students to choose one of their current reading assignments to use to complete this activity. It could be a page from a textbook, a current literature requirement, or even a newspaper or magazine article. Then take a piece of paper and fold it in half. To make the assignment more interesting, use something other than standard notebook paper, like construction paper, or legal-sized paper. Label one column “pronouns” and the other “antecedents.” Read the selected page, and list all the pronouns you can find along with their antecedents. What Is Wrong With This Sentence? Students in grades three and up should be given consistent practice recognizing correct pronoun-antecedent agreement. Write sentences on the board containing pronoun-antecedent agreement errors. The sentences could include errors in number (“A student left their lunch on the bus”) or gender (“My sister rode his bike to school”). Sentences can also cause problems with an ambiguous antecedent, such as this example: “The suitcase contained three shirts, two pair of pants and a dog bone. It belonged to my grandmother.” Call students up to the board to rewrite the sentences for correctness and clarity. - Creatas Images/Creatas/Getty Images

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The resources in this KS1 Maths classroom area help children to develop their knowledge of the different areas of Maths through mental and oral activities. Within the KS1 Maths Number and The Number System section children learn about counting, reading and writing numbers, number order and place value, estimating and rounding, fractions, number patterns and sequences. The Calculations area helps Key Stage 1 children with addition and subtraction, mental calculations, times-tables and checking sums. Children can learn about different types of measurements in the Measures section, including length, mass, capacity, time, area and money. Children can carry out the @school assessment tests to test their knowledge of the different areas of KS1 Maths. The resources and activities in the KS1 Maths section are in an interactive, online, or printable format that brings a differing dynamic to the subject for children studying at Key Stage 1. Dienes Blocks - Interactive test about Tens and Units. Dienes Blocks - Interactive activity where you need to use Dienes blocks to represent numbers. Even Numbers - Test about odd and even numbers. Number - Interactive test about finding odd numbers. Number 1 - Fill in the missing number for this interactive sum activity. Number 2 - Work out what the highest number is on the number grid with this test. Number Circles - Online test to find two numbers that add up to 14. Number Cross - Interactive test about missing numbers in a number sequence. Number Line - Interactive test to answer various sums using a number line. Number Line 1 - Interactive test to find the missing number from this sequence. Number Order - An online activity to help ordering a set of 2 digit numbers. Number Order 2 - Interactive test about ordering numbers. Number Pattern - A test for recognising number patterns. Number Sequence - Interactive test to fill in two numbers in a number sequence. Number Sort - Interactive test to sort numbers under certain criteria. Odds - An interactive test to find odd numbers.

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By Suzie Hill, M. Ed. Pronouns are words that take the place of common and proper nouns in a sentence. No matter how simple this seems, getting students to understand and be able to apply this knowledge is not always so easy. Here are a few fun ideas for teaching pronouns in the classroom that are sure to keep your students actively engaged. When introducing any of the activities, have a readily available list, similar to the one below, of pronouns for students to use as a reference. Personal pronouns are used in place of a common or proper noun. Example: He is not staying. Possessives show ownership. Example: This is his book. A relative pronoun links two pronouns into one complete thought or statement. Example: Bob is the man who built this house. Reflexives are used when the object of the sentence is the same as its subject. Each personal pronoun has its own reflexive pronoun. Example: I did not want to hurt myself . Activity 1: Pronoun Substitution Materials: Various objects (balls, blocks, books, games), pictures of proper nouns (famous people, places, and things), sentence strips, writing instruments (pens, pencils, markers, crayons), and chart paper or notebook paper. - Place objects and pictures around the room where students can easily see them. - Number each object/picture and have a sentence strip for each object/picture that either describes or begins a story about the object/picture. For example, with a soccer ball you might write on the sentence strip, "Michael likes to kick the soccer ball." - Have students rewrite the sentence using the appropriate pronouns. For example, "He likes to kick it." - After all students have a chance to write several sentences/paragraphs using appropriate pronouns, allow some time for them to share and identify aloud the pronouns they have on their papers. - For older students, or after students are beginning to master pronouns, have students use the sentences as a writing prompt and continue writing a paragraph or essay using appropriate nouns and pronouns. - Put items in bins around the room and set up "stations" so that students are able to move around the room and write. - If you have access to a SMART® Board or Promethean® Board, simply display the objects/pictures and sentences on the board. Activity 2: Pronoun Find Materials: Photographs and/or pictures cut out from magazines, writing paper, and pencils, pens, or markers. - Allow students to choose several pictures and/or photographs. Have them write one sentence describing the photograph/picture using nouns and one picture describing the same photograph/picture using pronouns. - Have students pair up and read their sentences aloud to each other. Have them tell each other the pronouns that can replace the nouns. - For older or more advanced students, have them write paragraphs or essays using the same format as the sentences. - Have students discuss when it is appropriate to use pronouns. For example, you would not use a pronoun to begin a story or paragraph because the reader would not know to whom the writer is referring. Activity 3: Pronoun Identification Materials: A piece of writing to read aloud that uses many pronouns. - For a fun way to review pronouns, read aloud to the whole class from a book or magazine. - Instruct students to clap their hands every time they hear you say a pronoun. - For older or more advanced students, choose a different action for each type of pronoun. For example, clap for personal pronouns, snap for possessive pronouns, stomp for relative pronouns, and wave for reflexive pronouns. Burgess, R. (2000). Laughing Lessons: 149 2/3 ways to make teaching and learning fun . Minneapolis, MN: Free Spirit. Tate, M. (2005). Worksheets don't build dendrites . Thousand Oaks, CA.

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Source: All images created by Amanda Soderlind In this lesson today, we are going to talk about the cytoplasm of a cell and discuss its structure and function within the cell. So the cytoplasm is the part of the cell that fills the space between the plasma membrane and the nucleus. So I have a picture of a cell over here. We have our plasma membrane on the outside of the cell and our nucleus in the middle or inside of the cell. So the cytoplasm is everything that fills that space between the plasma membrane and the nucleus. So it includes all of the organelles as well. So when we're discussing the cytoplasm, we're talking about the inside of the cell, everything within the cell except for the nucleus. The jelly-like fluid of the cytoplasm is called the cytosol. So if we're talking just about this jelly-like fluid-- we're not talking about any organelles. If we're discussing just the jelly-like fluid that fills the inside of the cell as part of the cytoplasm, it is called the cytosol. The cytoplasm is made up mostly of water. And, like we said, it contains all of the cell organelles, including the cytoskeleton. And also, many chemical reactions and processes happen within the cytoplasm. So it has a very important role in the cell in order to contain all of those organelles. It acts as sort of like a cushion for the organelles. There's several different ions and proteins dissolved in it that help in chemical reactions. And many of these reactions and processes will actually take place within the cytoplasm, as I mentioned earlier. So we're going to talk a little bit about the cytoskeleton now. And the cytoskeleton is a part of the cell contained in the cytoplasm that acts as structure and support for the cell. So think of your skeleton, for example, and the role that your skeleton plays. It acts to support your body and give your body structure. And this is similar to the cytoskeleton of a cell. It has kind of some of the same roles. It acts as structure and support for that cell. It helps it to maintain its shape and support the cell as a whole. So the cytoskeleton is composed of three different parts, the microtubules, microfilaments, and intermediate filaments. So these are the three parts of the cytoskeleton. The microtubules are these structures right here. And the microtubules are the largest parts of the cytoskeleton. And they move cell parts, and they help to organize the cell. So this is what a microtubule might look like in a cytoskeleton. Microfilaments have this structure here. And microfilaments act to reinforce parts of the cell, and they also help to anchor membrane proteins. And the intermediate filaments, this structure here, are the third part to our cytoskeleton. And intermediate filaments help to add strength. So they're adding strength to the cytoskeleton, allowing it to be more strong. And they also help to anchor actin and myosin, which you'll learn in later lessons are an important part of muscle contractions. So the three parts of our cytoskeleton are microfilaments, intermediate filaments, and microtubules. So this lesson has been an overview on the structure and function of the cytoplasm, as well as an introduction into the structure and function of the cytoskeleton. The jellylike fluid that supports the contents of the cell - found between the plasma membrane and the nuclear envelope The protein structure that provides support to the cell - much like the bony skeleton supports the human body The liquid found inside the cytoplasm that is mostly composed of water

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Explore patterns, properties and relationships and propose a general statement involving numbers or shapes; identify examples for which the statement is true or false Find the correct number in a sequence. Lots of choice over level, count forwards or back, count in whole numbers, multiples of 10, multiples of 100, decimals and fractions. |Sequences Fractions and Decimals|| Count on and back in decimal steps and fractions. Identify and continue sequences involving shape, colour and numbers. |Fractions Shape Sequences|| Recognise and continue the sequences involving fractions, shapes and colours. Lots of control over level including unit fractions and improper fractions. Extend children by choosing harder levels which require extending the sequence by finding general rules. |Numbers on a Carroll Diagram - Missing Labels|| Drag the correct labels onto the Carroll diagram. A great game to encourage reasoning about the properties of numbers. Works really well as a mental starter. An incredibly versatile teaching tool. You can change the start number and change the step size, then try and find the hidden number. Choose from several difficulty levels. Ask the children to discuss the different methods they could use to find the missing number. Can be used to explore sequences (including negative numbers and decimals), multiplication tables, as well as reasoning about numbers. |Sorting 3D Shapes on a Venn Diagram|| Use a Venn diagram to sort a variety of 3D shapes according to their properties, including: whether they are pyramids or prisms, the number of faces, edges and vertices and whether they have a curved surface. |ITP Number Grid|| View full screen in your browser. This ITP generates a 100 square. Choose a colour or the grey mask. You can then click on individual cells to hide or highlight them in different colours, and by clicking on the box at the left-hand foot of the grid and using the pointers you can hide or highlight rows and columns. The prime numbers and multiples can also be highlighted. This resource is freely available to download from the archived Primary Framework site.

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Moraines are deposits of gravel-like soil, rocks and even boulders left by the movement of glaciers. Such deposits are generally conspicuous because they are out of place: boulders on flat plains, rocks and gravel that differ from surrounding types, suggesting a remote origin. Moraines frequently scoop the Earth as they move, leaving a wide groove-shaped pattern. In the late 1700s, when geology was an emerging science, the prevailing belief was based on the Biblical myth that the Earth was only a few thousand years old. Evidence from moraines did much to discredit that view. As the first geologists began to investigate rock formations in England and other regions, they discovered unusual rocky debris and other indications that glaciers had once covered the land that was now bare. One of the first to realize that moraines were the product of ancient glacial movement was James Hutton, the “father” of geology and the author of the new concept of “deep” geological time. From his examination of rocky deposits and scraping patterns on cliffs, Hutton deduced that ancient glaciers must have moved over vast distances, picking up material in one region and depositing it thousands of kilometers away. Hutton’s (1795) ideas were treated as heresy in the Eighteenth Century, when moraines were interpreted as proof of the Biblical flood. It was not until the mid-nineteenth century that a majority of scientists accepted the idea of an ancient Earth and the evidence of a remote ice age.

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Electrical charges can move easily in some materials (conductors) and less freely in others (insulators), as we learned previously. We describe a material's ability to conduct electric charge as conductivity. Good conductors have high conductivities. The conductivity of a material depends on: - Density of free charges available to move - Mobility of those free charges In similar fashion, we describe a material's ability to resist the movement of electric charge using resistivity, symbolized with the Greek letter rho (ρ). Resistivity is measured in ohm-meters, which are represented by the Greek letter omega multiplied by meters (Ω•m). Both conductivity and resistivity are properties of a material. When an object is created out of a material, the material's tendency to conduct electricity, or conductance, depends on the material's conductivity as well as the material's shape. For example, a hollow cylindrical pipe has a higher conductivity of water than a cylindrical pipe filled with cotton. However, shape of the pipe also plays a role. A very thick but short pipe can conduct lots of water, yet a very narrow, very long pipe can't conduct as much water. Both geometry of the object and the object's composition influence its conductance. Focusing on an object's ability to resist the flow of electrical charge, we find that objects made of high resistivity materials tend to impede electrical current flow and have a high resistance. Further, materials shaped into long, thin objects also increase an object's electrical resistance. Finally, objects typically exhibit higher resistivities at higher temperatures. We take all of these factors together to describe an object's resistance to the flow of electrical charge. Resistance is a functional property of an object that describes the object's ability to impede the flow of charge through it. Units of resistance are ohms (Ω). For any given temperature, we can calculate an object's electrical resistance, in ohms, using the following formula: In this formula, R is the resistance of the object, in ohms (Ω), rho (ρ) is the resistivity of the material the object is made out of, in ohm*meters (Ω•m), L is the length of the object, in meters, and A is the cross-sectional area of the object, in meters squared. Note that a table of material resistivities for a constant temperature is given to you at right. Let's try a sample problem calculating the electrical resistance of an object: Question: A 3.50-meter length of wire with a cross-sectional area of 3.14 × 10–6 m2 at 20° Celsius has a resistance of 0.0625 Ω. Determine the resistivity of the wire and the material it is made out of. Question: At 20°C, four conducting wires made of different materials have the same length and the same diameter. Which wire has the least resistance? Answer: (2) gold because it has the lowest resistivity.

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- slide 1 of 3 Periodic Table Bingo If you’re teaching your students about the periodic table, try using this chemistry game to review what you’ve taught. Give out a blank Bingo sheet to each student, or have them make their own. Provide each student with a periodic table. Then have students select random elements from the periodic table and insert them into the squares of their Bingo sheet, leaving the middle square as a “wild" square. Then call out clues that point to a specific element which can be identified by understanding the periodic table, such as “a noble gas that has two full shells of electrons." Encourage students to identify the element and place a marker on that element if they have it on their Bingo sheets. The first student to fill up their sheet wins! - slide 2 of 3 Who Am I? This chemistry game works well for any lesson that includes a lot of terms. With students, brainstorm a list of these terms on the board. Then give one student a definition, or a clue to a specific term, and have that student identify which term you are referring to. For example, you might say “When something dissolves into me, we become a solution." If that student answers correctly, she can take a turn making up a clue for another student. If not, choose another student and try again. - slide 3 of 3 In the mood for more physically active chemistry games? Try this game to review the filling of electron shells. Split the class into two or more groups, and give each group stacks of chairs and a large amount of space. When you call out the name of an element, each group should hurry to arrange the chairs in the necessary number of electron shells, with one student occupying each chair that would represent an existing electron. Begin with elements that have lower atomic numbers, such as Lithium, which would only have two filled electrons in the inner shell and one in an outer shell.

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Reason for Alignment: This lesson brings all the Venn diagram activities together with some thorough discussions on sets and Venn diagrams specifically. There is a good worksheet as well. The discussions in the lesson do get to the main points of the textbook better than the activities would alone. Arithmetic: Students must be familiar with the following concepts: whole numbers/integers/natural numbers constant vs. variable Technological: Students must be able to: perform basic mouse manipulations such as point, click and drag use a browser for experimenting with activities Students will need: Access to a browser Pencil and paper A member of or an object in a set A set is a collection of things, without regard to their order A diagram where sets are represented as simple geometric figures, with overlapping and similarity of sets represented by intersections and unions of the figures Focus and Review Introduce students to the concept of sets. Consider leading students in discussions on the topic: If students are already familiar with the concept, consider asking guiding questions to activate What is an example of a set? [Answers will vary] Let's use whole numbers as an example. What do we call the number 5? [an element of the set of whole numbers] Let's think of another set that will have some (but not all) elements in common with whole numbers. What do we call the elements they have in common? If students are unable to answer any of the questions, tell them that they will learn more about that in this lesson. Be sure to ask those questions again in the closure. Let the students know what it is they will be doing and learning today. Say something like this: Today, class, we will be talking more about sets and what it means to be an element in a set. We are going to use the computers to learn about sets and Venn diagrams, but please do not turn your computers on or go to this page until I ask you to. I want to show you a little about sets and Venn diagrams first. You should first lead the students in a short discussion about Venn Diagrams. Ask students how sets and Venn Diagrams are interrelated. Ask students if these Venn Diagrams are dealing with sets as well. Explain to the class (or have students explain to each other) that all Venn Diagrams display different sets, even if the sets do not contain numbers. Open your browser to Venn Diagrams in order to demonstrate this activity to the students. Begin to explain the applet to the students by showing them the first example on the page. Ask the class if they know what the answer is. When a student has responded correctly, show the class that by clicking in the appropriate section of the diagram, the circles representing the sets will change color. Show the students the location of the "Check Answer" button and check the students' answer Try another example, letting the students direct your moves. Or, you may simply ask, "Can anyone describe the steps you will take for this assignment?" If your class seems to understand the process for doing this assignment, simply ask, "Can anyone tell me what you will do now?" If your class seems to be having a little trouble with this process, do another example together, but let the students direct your actions: On the second example (which appears when the first answer is checked), ask the students which section of the Venn diagram the element belongs in. Check the answer with the class and, in the event it is incorrect, have the students suggest reasons for why the answer might be different from the one guessed. Allow the students to work on their own. Monitor the room for questions to be sure that the students are on the correct web site. Since many of the questions are not strictly math-related, explain to the students that they may not know the answers to some of the questions. If this should happen, they should do their best and move on. Lead the class in a discussion using the following guiding questions. If students do not give the correct answer the first time, guide the discussion so that they can discover what the correct Which questions were more difficult? [The ones with words they didn't understand.] Why do you suppose that is? [Answers will vary] What information do you need to be able to answer these questions? [You need to understand how each set is defined in order to know which elements go where in a This lesson can be rearranged in several ways if only one computer is available for the classroom: The teacher may do this activity as a demonstration. As each new Venn diagram is displayed, allow the students an opportunity to decide individually, or in groups, the solution to the question. After an appropriate time, try an answer from a group or individual and discuss why the answer was or was not correct.

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Prior Knowledge: So far your students have learned how to write equations, translate sentences into equations and equations into sentences, solve one-step equations using addition and subtraction, solve simple equations using multiplication or division and solve multi-step equations. Now they will learn to solve equations with variables on both sides of the equation. Common Core State Standards A.REI.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. A.REI.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 1 Make sense of problems and persevere in solving them. 5 Use appropriate tools strategically. - I can apply order of operations and inverse operations to solve equations - I can construct an argument to justify my solution process What is the difference in solving a regular equation and an equation with variables on both sides? Vocabulary: inverse operation, isolate, variable, constant, reciprocal, coefficient

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Social skills are one of the most important skill sets that develop throughout childhood and adolescence. They are specific behaviours such as smiling, making eye contact, asking and responding to questions, initiating conversation or play as well as giving and acknowledging compliments during a social exchange. These skills influence positive social and developmental outcomes, and also lay the foundation for future academic success, autonomy, interpersonal relationships, emotional awareness, and resilience. Recent studies have shown that certain social skills; such as self control, cooperation, empathy and assertiveness influence positive classroom behaviour. Researchers argue that because these skills promote a child’s ability to complete tasks and work independently they influence their ability to learn and contribute to better relationships with teachers and peers. The research also suggests that social skills contribute to academic success. How can I tell whether my child needs help developing their social skills? - Avoids social activities/school - Displays inappropriate responses to verbal and nonverbal cues - Has difficulty initiating/maintaining social interactions - Has difficulty making and maintaining friendships - Seems disinterested in social interactions - Uses little eye contact How can I help develop my child’s social skills? One of the most effective ways you can help develop your child’s social skills is by modelling appropriate social behaviours ... One of the most effective ways you can help develop your child’s social skills is by modelling appropriate social behaviours, providing opportunities for positive socialisations and by offering opportunities for your child to discuss their concerns with you. - Model positive social behaviour (e.g. greet shop assistants, be attentive during conversation, ask and respond to questions) - Offer suggestions on how to manage situations with peers - Provide opportunities for positive social engagement: Arrange playdates for your child. Enrol your child into structured social activities (e.g. drama class, a sport, art class, scouts, etc) - Promote your child’s autonomy and independence - Discuss issues such as teasing, bullying and exclusion with your child and brainstorm ideas to manage these situations with them. - Encourage and help your child develop the two components of learning-related social skills: interpersonal skills - such as positive peer interaction, sharing and respecting other children. Work related skills - such as listening, following directions, appropriate group participation, staying on task and organisation. Another important issue to remember is that some social deficits, such as significant language and communication delays, atypical or ritualistic play, and persistent worries about attending school and social events may also be a sign that your child suffers from social anxiety or a developmental disorder. If this is the case, it is important to discuss your concerns with a GP or psychologist. How can schools help with social skills? Social issues commonly arise in primary and secondary school for different reasons. New students take time to settle; established students often report difficulties within their friendship groups in terms of peer dynamics or resolving conflict with other same-aged peers. Referrals to the school counsellor or local private psychologist typically occur when parents are concerned about their child’s ability to make and maintain friendships. Schools can help students to develop social skills through activities designed to encourage listening skills, empathy and understanding. Effective activities for teachers to boost social skills include “Tell Me A Story” (6-12 years) and “The Likes of Youth” (9-16 years). Similarly, “Circle Time” is a regular meeting among students in the classroom setting on a daily or weekly basis. Students and teachers commonly experience positive outcomes with specialized program and resources when students have the opportunity to regularly practice pro-social behaviour. There are useful books for children aged 4-8 years to develop social skills such as the How to be a Friend: A guide to making and keeping friends. For children aged 7 to 12 years consider Learning About Friendship and The Social Skills Menu. Programs and workshops such as Quirky Kid Clinic’s ‘The Best of Friends’ are a great way to practice and develop social skill in a small group or large school setting. Information provided by the Quirky Kid child psychology clinic. Find out more about developing social skills at the Quirky Kid website.

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Pressure that shapes rocks to align in particular directions causes foliation, according to the Mineralogical Society of America. When such differential pressure acts on the forming rocks, it produces layers of rocks that run in parallel to each other, creating the diagnostic banded appearance of foliated rocks.Continue Reading Different degrees of pressure and heat result in unique forms of foliated rock. When submitted to light pressure and low heat, metamorphic rock forms slate, which is a fragile rock that tends to break at the joints of layers. This produces thin, flat rocks. Slightly higher pressures and temperatures produce phyllite, which is a harder rock that often has a shiny appearance. Phyllite often includes deposits of micas, which follow the direction of folliation, giving it its shiny appearance. Still greater pressures result in the formation of schist. Schist has a larger grain than phyllite, but it shares phyllite's shiny luster from large mica deposits. These deposits are often larger in schist than in phyllite. The greatest pressures and heats form gneiss. Gneiss has alternating bands of dark and light rock, which are formed when pressures form large mineral deposits into thinner bands. Gneiss has coarser bands than other foliated metamorphic rocks. Unlike phyllite and schist, gneiss contains very little mica. However, gneiss often contains quartz and feldspar.Learn more about Geology

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Compare and Contrast Graphs of Rational Functions Lesson 8 of 10 Objective: Students will be able to compare and contrast the graphs of rational functions in the form y=a/(x-b)+c and describe the differences and similarities of these graphs using academic vocabulary. There is an extended warm-up provided for today, which you can choose to use or not. The idea is that students can use the day to begin preparing for the summative assessment of this unit. The extended warm-up includes problems related to each key skill of this learning unit in the same sequence that they were covered during the unit. Direct students to choose the problems that they want to focus on because obviously 30 minutes is not enough time to tackle all of the problems. Some students may have fully mastered all of these skills during the unit, so the challenge warm-up is provided for them. Creating graphs to match the approach statements turns out to be quite difficult. If they accomplish this with graph sketches, you can ask them to find equations that would match those approach statements as well. This is incredibly challenging for some graphs, and will require some piece-wise functions. These questions require students to generate pairs of functions that fit the given requirements. It is like working backwards from the classwork. Some students might refer to problems on the classwork to find their examples. I would encourage them to try to generate their own examples first, and only refer to the classwork for confirmation or if they get stuck. It is important to discuss these problems as a class to make sure that students end the class with correct examples. Have them share with each other, or put up two sets of examples for each problem and ask them to decide which pair of functions matches the given requirements. The purpose of this discussion is two-fold: (1) to have students practice looking at the equations and identifying the key features of the graphs without actually graphing and (2) to use the key terms to describe the graphs of these functions more abstractly.

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The brain has an amazing ability to identify the source of sounds around you. When driving, you can tell where an approaching fire truck is coming from and pull over accordingly. In the classic swimming pool game of “Marco Polo,” the player who is “it” swims toward the players who says “Polo.” In the field of neuroscience, this ability is called sound localization. Humans can locate the source of a sound with extreme precision (within 2 degrees of space)! This remarkable feat is accomplished by the brain’s ability to interpret the information from both ears. So how does your brain do it? Neuroscientists have been working to understand the mechanisms of sound localization for many years, and they have identified two cues that are essential for sound localization in the horizontal dimension. Imagine there is a circle that makes a perfectly flat plane around your head, as shown below. When a sound comes from the speaker, how can you identify its location so accurately? In the 1790s, Venturi played a flute around people and asked them to point in his direction. He proposed that the sound amplitude (loudness) difference between the two ears was the cue used for sound localization. Much later in 1908, Malloch proposed that the time difference of the sound reaching each ear was the cue used for sound localization. Years later, neuroscientists found neurons in the auditory centers of the brain that are specially tuned to each cue: intensity and timing differences between the two ears. So, the brain is using both cues to localize sound sources. For example, sound coming from the speaker would reach your left ear faster and be louder than the sound that reaches your right ear. Your brain compares these differences and tells you where the sound is coming from! But what happens when a sound comes from anywhere along the midline of your head? It could be directly in the front of you, behind you, or above you. In any of these cases, there would be no difference in sound loudness or delay between your two ears! It turns out that your brain uses a third cue to locate sounds in the vertical dimension: the different frequency profile of sound caused by the size of your head and your external ear, called the pinna. The pinnae are exquisitely shaped not only to collect sound, but also to change the frequency profile of a sound. Depending on its origin, certain frequencies get enhanced, while others get attenuated. As shown in the picture below, freqnency changes in colors are tied to their locations. This cue is unique to each pinna and therefore monoaural. Neuroscientists have found neurons in the lower level of auditory brain that are tuned to these frequency notches as well. So, what happens when sounds are moving? Obviously, sounds become louder as they near us and softer as the move away, but the perceived frequencies of sound also change. For example, the frequency of the siren from a fire truck sounds higher as it moves toward us and lower as it moves away. This phenomenon was first discovered by the Austrian Physicist Christian Doppler, and is thus named the Doppler effect. The Doppler effect may be a cue for the perception of distance changes. Additionally, the brain tracks the vertical and horizontal angle by the binaural and monaural cues such as the three cues mentioned above. Overall, the brain uses a variety of cues to determine the location of a sound. Our current understanding of the mechanisms of sound localization is mostly limited to the cues themselves and how the lower levels of the brain’s auditory pathway process these cues. It is a really exciting time to explore how the higher level auditory brain uses those signals from lower levels to form the perception of the sound location! Written by Xiaorui “Ray” Xiong Phillips D.P., Quinlan C.K. & Dingle R.N. (2012). Stability of central binaural sound localization mechanisms in mammals, and the Heffner hypothesis, Neuroscience & Biobehavioral Reviews, 36 (2) 889-900. DOI: 10.1016/j.neubiorev.2011.11.003 Letowski T.R. and Letowski S.T. (2012) Auditory Spatial Perception: Auditory Localization, Army Research Laboratories ARL-TR-6016 Images adapted from Crowd At Busy Street by Petr Kratochvil, 123rf, Wikimedia Commons, clker, and Grothe B., Pecka M. & McAlpine D. (2010). Mechanisms of Sound Localization in Mammals,Physiological Reviews, 90 (3) 983-1012. DOI: 10.1152/physrev.00026.2009.

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Students learn to write equivalent fractions that represent the shaded part of given figures. Students also learn that multiplying or dividing the numerator and denominator of a given fraction by the same number results in an equivalent fraction. For example, multiplying the numerator and denominator of 5/12 by 2 results in the equivalent fraction 10/24. Students are also asked to find the value of the variable that makes given fractions equivalent. For example, if 3/7 = 9/d, then the value of d that makes the fractions equivalent is 21.

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Introduction to Angles Lesson 2 of 5 Objective: SWBAT identify the number of angles for a given two-dimensional shape. We are going to review our 2D shapes by playing a quick game of "Who am I?". I divide students into pairs and give each pair a deck of "Who am I?" cards (these have a list of attributes for a shape and the question "Who am I?". One student holds up a card and reads it to their partner. Their partner then explains what the shape is and defends their answer by describing shape attributes. If students have not played this game before (my students have), model how to play in front of the class for maximum impact. I allow students to play the game for 5-7 minutes before bringing students back together for the introduction to new material. Introduction to New Material I start class by drawing a picture of a square on the board. This square has four angles. I write this definition on the board: Angle: the place where two lines intersect or come together. Show students a variety of other shapes (trapezoid, hexagon, parallelogram, etc.) and ask them how many angles each one has. Show students a square (right angle), a trapezoid (acute angle), and a hexagon (obtuse angle). Circle the appropriate angles. Turn and talk: How are these angles similar or different? Students might say that the angle on the trapezoid is small and the angle on the hexagon is big. They might say the angle on a square looks like an L. We are going to learn some vocabulary to explain angles. Then, I add to the angles anchor chart Right angle: A corner angle (Draw or paste pictures of a right angle). Acute angle: An angle that is less than a right angle (Draw or paste pictures of shapes with acute angles) Obtuse angle: An angle that is greater than a right angle (Draw or paste pictures of obtuse angles) . As a check for understanding, I show students some pictures of shapes and have them explain why they think they are right, acute, or obtuse. I start the guided practice by handing white boards and white board markers to every student. I give the following prompts and have students draw the shapes on their white boards. After each prompt, I have at least one student share why they drew their shape. 1) Draw a shape that has four angles. (multiple correct answers: have students explain their answers!) 2) Draw a shape that has zero angles 3) Draw a shape that has three angles 4) Draw a shape that has six angles 5) Draw a shape that has acute angles 6) Draw a shape that has at least one right angle 7) Draw a shape that has at least one obtuse angle Independent practice is tiered based on understanding of this concept. I determine groups based on performance during the guided practice and general geometrical understanding. Group A: In need of intervention Students works in partners to draw shapes according to their angles. Group B: Right on track! Students work in partners to draw shapes according to their angles. This group also has one practice work sheet about right, acute, and obtuse angles. During the independent practice, I circulate focusing most of my attention on my intervention group to support students as they draw their shapes and to check for understanding. After students have finished their independent practice, I bring them back together and go over a few of the questions, cold calling students to share and defend their answers. This closing serves as a chance for me to check student understanding and gives students a chance to share their knowledge and gain confidence talking and thinking about angles.

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Science fair projects are a kid's introduction to the world of experimentation. While kids are used to hearing about science in class, science fair projects are an opportunity to tackle a question of their own choosing by designing their own experiment. For many kids, the topic of this experiment may be driven by their time in recess: the bouncing height of a ball. The basis of a science fair project on the bouncing height of a ball will be an examination of two concepts in physics. One is Newton's third law of motion: for every action there is an equal and opposite reaction. For a bouncing ball, the action is a ball falling against the ground with a force that is determined by the mass of the ball and the height from which it fell. The ground will then apply this same force to the ball, which causes the ball to bounce back up. When the ball is falling to the ground, gravity is pushing the ball down. When the ball bounces back up it is using its force to overcome gravity, which is trying to push the ball back down to the ground. Consequently, it will take more force than the ball bounced with to return the ball to the height from which is originally fell. Once the ball has used up its force in overcoming gravity, it will begin to fall back to the ground. It will then bounce with a force determined by the most recent height from which it fell, which will cause it to bounce to a lower and lower height. It will stop when the force of the bounce is no longer sufficient to even overcome the force gravity exerts on the ball. The basis of every experiment is a question. When it comes to the bouncing height of a ball, these questions should be those that collecting and analyzing data on the height to which balls bounce can answer. Some examples of these can be "dDo balls of different material lose bouncing height at the same rate?" or "Do balls lose bouncing height at different rates if they are dropped from different heights?" For the experiment, you should have a staff or large board with clear lines marking measurement intervals behind the bouncing ball. Because science values accuracy, and estimating the height of a bouncing ball in real time is a bit of a dicey proposition, you should have a camera that can see the ball and the measuring device behind it record your different trials. This way, you can review the footage later to accurately determine the moment at which the ball reached its maximum bounce height. By consulting the ball's position relative to the measuring device behind it in the recording, you can then record a more accurate measurement of the ball's height.

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How Do We Measure? Comparing Weight Day 2 Lesson 15 of 18 Objective: Students will be able to describe objects in terms of weight and compare the weight of two objects. Problem of the Day Today's Problem of the Day: Look at these snakes. Compare their lengths. For this Problem of the Day, I include two pictures of snakes. They are the same graphic with slight changes in color and size. The snakes are movable. I have one student answer this question, and explain his or her thinking. If the student does not do it, I encourage the student to move the snakes to ensure that he or she has enough information to compare the length of the two snakes. I am looking for the student to line up the two snakes on one end so that the difference in length is easily seen. I am also looking for students to use the words longer and shorter as the comparison of length is explained. Presentation of Lesson I have the students move to the perimeter of the carpet. I use the word perimeter to reinforce some additional mathematical vocabulary. I remind students that when we are working with materials in the middle of the carpet, we need to keep our hands in our laps and not touch the materials unless asked by the teacher. I place a balance in the middle of the carpet. Near me I also have a bucket containing the following: a feather, a board book, a pencil, an apple, a bar of soap, and a can of soup. This is a new tool that we are going to use in our math lesson today. Does anyone know what this is for? This is called a balance, and we use it to help us compare the weight of objects. When we place an object in each side, one side goes up and the other side goes down. Let's try it out. I call up a student to put a feather in one side and another student to put small board book in the other side. Which object went up? The feather went up, so that tells us that the feather weighs less. We call this lighter. Which object went down? The book went down, so that tells us that the book weighs more. We call this heavier. We continue with the other objects. I start with large differences in weight (feather/book, pencil/apple). I also show the students a very close comparison using the apple and the bar of soap. Depending on the size of the apple and soap, they may almost be equal. I discuss with student how, just like length, the weight of two objects can also be equal. We don't always have a balance to use to compare the weight of two objects, but sometimes we can figure it out just by holding the objects in each of our hands. When I hold the soup can in one hand and the feather in the other hand, I can feel that the soup can is heavier. I tell students that they are going to be comparing some of their own objects and recording their results on a Comparing Weight worksheet. You are going to be doing this paper with the people at your table, but we are going to go over the directions together. When you get to your seat, do not touch your container of objects. You need to get out a pencil and put your name on your paper. When your name is on your paper hold your pencil in the air, that will let me know that you are ready to start. I use the procedures outlined here on the Paper Procedures. Prior to this lesson, I placed a plastic container at each table containing the following materials: a crayon, a marker, a die, a foam ball, an apple, a bar of soap, a bottle of glue and a full water bottle. Compare the weight of the objects shown. Circle the object that is heavier. Put an X on the object that is lighter. The first thing the directions tell you to do is compare the weight of the objects shown. You are going to do this by holding one in each hand. You will then mark your answers on your paper using an X for the lighter object and a circle for the heavier object. Look at the example in the box. When I hold a feather in one hand and a can in the other, I can feel that the feather is lighter and the can is heavier. I need to put and X on the feather and circle the can. You are going to share objects with the people at your table. Flip your paper on the back. The last question asks you to choose two objects and compare their weight. You need to the draw the items and mark them with an X or circle based on your comparison. I walk around and make sure that students are sharing the objects and are actually feeling the objects before they mark their answers. I look for students who are using the words heavier and lighter as they talk with their group. The centers for this week are: - Measuring Abe's Hat (from Teachers Pay Teachers) - Measure the Room (from Teachers Pay Teachers) - Valentine's Day Measurement (Teacher Created Resource- Use candy hearts) - Teen Numbers with Ten Frames (from Teachers Pay Teachers- Use buttons) - SMARTBoard (2D and 3D Shapes from Starfall) I quickly circulate to make sure students are engaged and do not have any questions about how to complete the centers. I pull three groups during centers and work with them depending on the time they need (5 - 10 minutes). Today I am focusing on teen numbers with all of the groups. Based on the end of unit assessment for teen numbers and report card assessments that I am currently working on, I have found that my students are still struggling with teen numbers. They have caught on to measurement quickly, so I feel that it is important to use this small group time to practice identifying teen numbers and counting groups of up to 20 objects. I group the students by ability level based on the assessments I mentioned above, but I do the same activity with all three groups. I start with teen number flashcards. I then give each student a number card and the student counts out that number of objects. Finally, I say a teen number and have each student write it on their white board. Prior to clean up, I check in with each table to see how the centers are going. I turn on Tidy Up by Dr. Jean. Students clean up and return to their seats. This is a paid resource, but there are many free examples of transition songs easily found in a web search. Another transition I have been using lately during clean up has been counting down from 20 slowly. The students like to count backwards with me as they clean up and I can lengthen or reduce the clean up time based on how students are doing and how much time we have. To close, I choose a student paper to display on the document camera while that student explains their work. I have the student focus on their chosen comparison - in this case the number 7. I mention positive things noticed during centers as well as something that needs to be better next time. I review what we did during our whole group lesson. Today we learned to compare objects based on weight. Tomorrow, we are going to continue to practice comparing objects based on weight.

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Antibodies (also referred to as immunoglobulins and gammaglobulins) are produced by white blood cells. They are Y-shaped proteins that each respond to a specific antigen (bacteria, virus or toxin). Each antibody has a special section (at the tips of the two branches of the Y) that is sensitive to a specific antigen and binds to it in some way. When an antibody binds to a toxin it is called an antitoxin (if the toxin comes from some form of venom, it is called an antivenin). The binding generally disables the chemical action of the toxin. When an antibody binds to the outer coat of a virus particle or the cell wall of a bacterium it can stop their movement through cell walls. Or a large number of antibodies can bind to an invader and signal to the complement system that the invader needs to be removed. Antibodies come in five classes: - Immunoglobulin A (IgA) - Immunoglobulin D (IgD) - Immunoglobulin E (IgE) - Immunoglobulin G (IgG) - Immunoglobulin M (IgM) Whenever you see an abbreviation like IgE in a medical document, you now know that what they are talking about is an antibody. For additional information on antibodies see The Antibody Resource Page.

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The last topic in our chemistry unit has been about Bohr Diagrams. We’ve been talking for the last week or so about the organization of the periodic table. Elements are organized by - atomic number - how many electrons are in the outer shell - by which shell is their valence shell (or the shell that electrons are added to) - Columns tell us how many atoms are in the outer shell. - Rows tell us how many shells there are. - The atomic number tells us how many electrons an atom has. But to really understand this better, I thought the kids should actually draw in the electrons using the Bohr Diagram model. We used examples from the first four rows. If anyone else can use these Bohr Diagram worksheets, they are free to download. Early next week, I’ll share all the resources we used for our Periodic Table Unit. Other chemistry posts that may be of interest: - Chemistry Unit: A Study of the Periodic Table (Coming soon) - Chemistry Experiments for Kids (Grade 2) – Matter is Neither Created Nor Destroyed — Acids and Bases - Chemistry Experiments for Kids (Grade 2) – Mixtures, Chromatography, DNA Kit - Explosion of Colors in Milk Experiment and Other Chemistry Fun! - Chemistry Unit: The Size of Atoms - States of Matter: Solid, Liquid, Gas — Learning Activities - Chemistry: Molecule Movement Experiment and Chemistry Review Worksheet These notebook pages are free. - Science Experiments: Water Molecule Attraction - Building Molecules Chemistry Activity This also has some free notebook pages about building molecules: See you again soon here or over at our Homeschool Den Facebook Page! ~Liesl Don’t miss out on future printables and packets; subscribe to our Homeschool Den Newsletter. Don’t forget to confirm in your inbox!

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The worksheet that you can download by clicking the text above deals with a range of intervals (to give you a flavour of what we do) but in reality musical intervals should be introduced to our students gradually and during the early stages of a study of music theory they need only really concern themselves with whole-step and half-step intervals. The material below looks at the stage where those first two intervals should be studied are introduced to students. Before studying these intervals learners should be completely familiar with the first topic involved in of Music Theory which is aimed at developing the ability to name any musical note correctly and confidently. We study whole-step and half-step intervals first because an understanding of those two intervals is all that is required before being able to construct and analyse Major and minor scales. When students develop an understanding of scales then all intervals can be studied in relation to those scales An understanding of music theory must be built up from solid foundations and before looking at developing an understanding of intervals students must first be confident that they can "correctly" name notes Click this text for a FREE Note Naming Worksheet When they can name notes correctly and confidently then they are ready to move on to look at how intervals (the "gaps" between notes are defined and created. If we do not pay sufficient attention to these early lessons then our students will forever struggle when it comes to developing a functional and "joined up" knowledge of music theory Unless a student can be made to understand the two most important intervals (whole and half steps) then they can't be expected to understand how scales work? If they don't understand scales then they won't be able to grasp chord construction? If they struggle with chord construction then they are not going to understand established harmonic systems and the relevance of key signatures? Our resources are designed to allow you to help students to build a "joined up" knowledge of music theory from a solid grounding in the basics Our materials that cover the early stages of music theory are designed to allow your students to progress logically through the "nuts and bolts" of the subject without getting too hung up on notation. After they have mastered the principles behind correctly naming notes students are ready to go on to study intervals of a whole-step and a half-step Note Naming How to correctly identify notes Intervals (particularly whole and half steps) Intervals into Scales (how intervals of whole and half steps combine to create scales) Scales into Chords (how scales contain chords within them and the difference between major and minor chords) Chords into Harmonic Systems (chords which "fit" together that can be created from within a single scale) If you click the image below you will get a Free PDF containing 20 pages of lesson plans looking at the early stages of teaching music theory in much greater detail than we can go into here Click this text for a FREE 20 Page set of Music Theory Lesson Plans Covering Intervals and Beyond Our "one click" download consists of 300 professionally prepared handouts that can be printed over and over again for less than the price of a single paper textbook! many of which deal with the correct identification of intervals These resources are especially designed to make life easier for classroom music or instrumental teachers who need to get theoretical ideas over to students. The handouts have been put together so that the same basic ground can be covered with differing levels of graphic support (some handouts feature keyboards and have space for letter names while others aimed at more advanced students rely on a more conventional musical stave approach). They are designed so that a single music educator might work with all ability levels within a single session. challenging the more able learners whilst supporting those who are not so familiar with the concepts and material under study musicteachingresources.com is a new sister site of the already well established guitar and bass teacher's resources website teachwombat.com Diatonic Harmony provides a framework by which music students can develop an understanding of all of the chords to be found in any particular key. An understanding of the diatonic system will allow students to examine a chord sequence and to decide which scale it is based upon as well as to give them the knowledge to compose musically "correct" chord sequences of their own. Once an understanding of the diatonic system has been developed students are ideally placed to work on study of the (relatively few) common alterations to the diatonic chords which provide the chords that make up the bulk of popular music. A feature of the materials relating to the development of an understanding of the system is a series of "diatonic puzzles" (click the image to download a free sample worksheet) that contain all of the diatonic chords from a particular key (in the case of the free sheet the key is D) Stdents are invited to firstly identify the chords on the worksheet and then to name the key that all of the triads belong to. It is likely (and desirable) that as they progress through the sheets they will begin to develop an ability to identify the key before they have named all of the chords on the sheet by using an increasing understanding of the system and the chords within it. An example of this understanding might be that they come to realise (rather than just be able to recite) that chord no VII is always a diminished chord (in the case of the sample sheet C# diminished) and that the tonic (name) chord of the key is a major chord a semitone above the root of chord no VII (a D chord?) Another example would be that two major triads a tone apart might be identified (G and A on the free worksheet)? Armed with this information students would be able to deduce the key containing all of the chords on the sheet by correctly identifying the lower of these major triads (G) as chord IV (the subdominant) and the higher one (an A chord) as Chord no V ( the dominant chord) As there is only one Major key (in this case D) which features these two chords then identification of the parent key could become fairly simple by addressing the following questions Which scale has a fourth note of G (the root note of a G major triad)? Material relating to the diatonic system forms part of our package that music teachers can now download featuring 200 professionally prepared handouts that can be printed over and over again and all for less than the price of a single textbook! These resources are especially designed to make life easier for classroom music teachers and instrumental instructors. They have been put together so that a single music educator might work with all ability levels within a single session or work back to basic principles with an individual student.

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Definitions in this text: Essentials, Section 1 Basic Concepts of Economic Value This section explains the basic economic theory and concepts of economic valuation. Economic value is one of many possible ways to define and measure value. Although other types of value are often important, economic values are useful to consider when making economic choices – choices that involve tradeoffs in allocating resources. Measures of economic value are based on what people want – their preferences. Economists generally assume that individuals, not the government, are the best judges of what they want. Thus, the theory of economic valuation is based on individual preferences and choices. People express their preferences through the choices and tradeoffs that they make, given certain constraints, such as those on income or available time. The economic value of a particular item, or good, for example a loaf of bread, is measured by the maximum amount of other things that a person is willing to give up to have that loaf of bread. If we simplify our example “economy” so that the person only has two goods to choose from, bread and pasta, the value of a loaf of bread would be measured by the most pasta that the person is willing to give up to have one more loaf of bread. Thus, economic value is measured by the most someone is willing to give up in other goods and services in order to obtain a good, service, or state of the world. In a market economy, dollars (or some other currency) are a universally accepted measure of economic value, because the number of dollars that a person is willing to pay for something tells how much of all other goods and services they are willing to give up to get that item. This is often referred to as “willingness In general, when the price of a good increases, people will purchase less of that good. This is referred to as the law of demand—people demand less of something when it is more expensive (assuming prices of other goods and peoples’ incomes have not changed). By relating the quantity demanded and the price of a good, we can estimate the demand function for that good. From this, we can draw the demand curve, the graphical representation of the demand function. It is often incorrectly assumed that a good’s market price measures its economic value. However, the market price only tells us the minimum amount that people who buy the good are willing to pay for it. When people purchase a marketed good, they compare the amount they would be willing to pay for that good with its market price. They will only purchase the good if their willingness to pay is equal to or greater than the price. Many people are actually willing to pay more than the market price for a good, and thus their values exceed the market price. In order to make resource allocation decisions based on economic values, what we really want to measure is the net economic benefit from a good or service. For individuals, this is measured by the amount that people are willing to pay, beyond what they actually pay. Thus, two goods that sell for the same price may have different net benefits. For example, I may have a choice between wheat and multi-grain bread, which both sell for $2.00 per loaf. Because I prefer multi-grain, I am willing to pay up to $3.00 for a loaf. However, I would only pay $2.50 at the most for the wheat bread. Therefore, the net economic benefit I receive for the multi-grain bread is $1.00, and for the wheat bread is only $.50. Economic values are also affected by the changes in price or quality of substitute goods or complementary goods . If the price of a substitute good changes, the economic value for the good in question will change in the same direction. For example, wheat bread is a close substitute for multi-grain bread. So, if the price of multi-grain bread goes up, while the price of wheat bread remains the same, some people will switch, or substitute, from multi-grain to wheat bread. Therefore, more wheat bread is demanded and its demand function shifts upward, making the area under it, the consumer surplus, greater. Similarly, if the price of a complementary good, one that is purchased in conjunction with the good in question, changes, the economic benefit from the good will change in the opposite direction. For example, if the price of butter increases, people may buy less of both bread and butter. If less bread is demanded, then the demand function shifts downward, and the area under it, the consumer surplus, decreases. Producers of goods also receive economic benefits, based on the profits they make when selling the good. Economic benefits to producers are measured by producer surplus, the area above the supply curve and below the market price. The supply function tells how many units of a good producers are willing to produce and sell at a given price. The supply curve is the graphical representation of the supply function. Because producers would like to sell more at higher prices, the supply curve slopes upward. If producers receive a higher price than the minimum price they would sell their output for, they receive a benefit from the sale—the producer surplus. Thus, benefits to producers are similar to benefits to consumers, because they measure the gains to the producer from receiving a price higher than the price they would have been willing to sell the good for. When measuring economic benefits of a policy or initiative that affects an ecosystem, economists measure the total net economic benefit. This is the sum of consumer surplus plus producer surplus, less any costs associated with the policy or initiative. Essentials, Section 2 – Valuation of Ecosystem Services

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We can capture and convert solar radiation into useful forms of energy, such as heat and electricity, using a variety of technologies. The technical feasibility and economical operation of these technologies at a specific location depends on the available solar radiation or solar resource. Basic principlesEvery location on Earth receives sunlight at least part of the year. The amount of solar radiation that reaches any one "spot" on the Earth's surface varies according to these factors: The Earth revolves around the Sun in an elliptical orbit and is closer to the Sun during part of the year. When the Sun is nearer the Earth, the Earth's surface receives a little more solar energy. The Earth is nearer the Sun when it's summer in the southern hemisphere and winter in the northern hemisphere. However the presence of vast oceans moderates the hotter summers and colder winters one would expect to see in the southern hemisphere as a result of this difference. The 23.5° tilt in the Earth's axis of rotation is a more significant factor in determining the amount of sunlight striking the Earth at a particular location. Tilting results in longer days in the northern hemisphere from the spring (vernal) equinox to the fall (autumnal) equinox and longer days in the southern hemisphere during the other six months. Days and nights are both exactly 12 hours long on the equinoxes, which occur each year on or around March 23 and September 22. Countries like the United States, which lie in the middle latitudes, receive more solar energy in the summer not only because days are longer, but also because the Sun is nearly overhead. The Sun's rays are far more slanted during the shorter days of the winter months. Cities like Denver, Colorado, (near 40° latitude) receive nearly three times more solar energy in June than they do in December. The rotation of the Earth is responsible for hourly variations in sunlight. In the early morning and late afternoon, the Sun is low in the sky. Its rays travel further through the atmosphere than at noon when the sun is at its highest point. On a clear day, the greatest amount of solar energy reaches a solar collector around solar noon. Diffuse and direct solar radiationAs sunlight passes through the atmosphere, some of it is absorbed, scattered, and reflected by the following: MeasurementScientists measure the amount of sunlight falling on specific locations at different times of the year. They then estimate the amount of sunlight falling on regions at the same latitude with similar climates. Measurements of solar energy are typically expressed as total radiation on a horizontal surface, or as total radiation on a surface tracking the sun. Radiation data for solar electric (photovoltaic) systems are often represented as kilowatt-hours per square meter (kWh/m2). Direct estimates of solar energy may also be expressed as watts per square meter (W/m2). Radiation data for solar water heating and space heating systems are usually represented in British thermal units per square foot (BTU/ft2). More informationEvaluating your site's potential for solar water heating Related category• SOLAR ENERGY AND POWER Home • About • Copyright © The Worlds of David Darling • Encyclopedia of Science • Contact

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We’ve all been stunned by images showing the dramatic retreat of mountain glaciers. Yet few of us have given much thought to what happens next. Now the first study to look at how life invades soil immediately after mountain glaciers melt has an answer. Primitive bacteria step in to colonise the area, enrich the soil with nutrients, and even cement the ground, preventing landslides, say researchers who have studied the process in the Peruvian Andes. A few studies have looked at the types of plants that colonise mountain valleys that were previously covered in ice. But before plants move in there is usually a period, which at high latitudes and altitudes can last several years, during which the newly uncovered soil appears totally barren (see picture, right). To investigate what is happening during this period, Steve Schmidt of the University of Colorado and colleagues examined the soil at the retreating edge of the Puca glacier in the Peruvian Andes. Between 2000 and 2005, they sampled the top 10 centimetres of ground that was revealed as the glacier moved uphill at a rate of 20 metres per year. They analysed the chemical structure of the samples and screened for bacteria. They found that over the years, the “oldest” soil â” the dirt taken from the point that was revealed at the glacier edge in 2000 â” changed rapidly. The first organisms to appear in the soil were cyanobacteria. These primitive bacteria are found in many marine ecosystems and some land-based ecosystems. It is these bacteria we have to thank for pumping oxygen into Earth’s atmosphere 3.4 billion years ago, allowing land life to evolve. By running DNA analyses on the soil, Schmidt and his colleagues show how the bacteria population changed over the first five years. Whereas “young” soil contained just three distinct genetic strains of cyanobacteria, four-year-old soil harboured up to 20. The cyanobacteria increased the amount of carbon available in the soil, through photosynthesis and, along with other types of bacteria, they also boosted nitrogen levels in the soil, an essential nutrient for plant life. Another, perhaps more surprising, function of the cyanobacteria seems to be to hold the ground together. Previous studies have shown that they secrete sugary chemicals that help hold the soil particles together and prevent erosion. At Puca glacier, the researchers found that soil shear strength was nearly double in the oldest soil relative to the youngest. “An important role of cyanobacteria in extreme environments may be to hold the soil in place,” say Schmidt and colleagues. Previously, it had been suggested that newly uncovered soil might draw its life from nutrients and bacteria deposited by wind, or from ancient carbon “pools” that were trapped beneath the glacier. Instead, the team say that though ancient carbon may help fuel the very early stages of new life, the cyanobacteria and nitrogen-fixing bacteria rapidly take the leading role. Journal reference: Proceedings of the Royal Society B: Biological Sciences (DOI: 10.1098/rspb.2008.0808) Climate Change – Want to know more about global warming � the science, impacts and political debate? Visit our continually updated special report.

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Hearing, or audition, depends on the presence of sound waves, which travel much more slowly than light waves. Sound waves are changes in pressure generated by vibrating molecules. The physical characteristics of sound waves influence the three psychological features of sound: loudness, pitch, and timbre. - Loudness depends on the amplitude, or height, of sound waves. The greater the amplitude, the louder the sound perceived. Amplitude is measured in decibels. The absolute threshold of human hearing is defined as 0 decibels. Loudness doubles with every 10-decibel increase in - Pitch, though influenced by amplitude, depends most on the frequency of sound waves. Frequency is the number of times per second a sound wave cycles from the highest to the lowest point. The higher the frequency, the higher the pitch. Frequency is measured in hertz, or cycles per second. Frequency also affects loudness, with higher-pitched sounds being perceived as louder. Amplitude and frequency of sound waves interact to produce the experiences of loudness and pitch. Timbre, or the particular quality of a sound, depends on the complexity of a sound wave. A pure tone has sound waves of only one frequency. Most sound waves are a mixture of different frequencies. The Structure of the Ear Knowing the basic structure of the ear is essential to understanding how hearing works. The ear has three basic parts: the outer ear, the middle ear, and the inner ear.

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K.CC.4 Worksheets, K.CC.4 Activities, K.CC.4 Worksheet, K.CC.4 Activity, K.CC.4 Standard, K.CC.4 Common Core, K.CC.4 Common Core Standard, K.CC.4 Lesson Plans, K.CC.4 Lessons, CCSS.Math.Content.K.CC.B.4, CCSS K.CC.4 Kindergarten Counting and Cardinality Standards Count to tell the number of objects. - K.CC.4. Understand the relationship between numbers and quantities; connect counting to cardinality. - When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. - Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. - Understand that each successive number name refers to a quantity that is one larger. Worksheets, Activities and Posters for this standard, along with all other Math and ELA Common Core Standards for Kindergarten, are included in the Kindergarten Common Core Workbook.

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"Oh, Oh, I Know the Answer!!" I. Rationale: Today we're working on the correspondence o_e= /O/. Students will learn /O/ by identifying the sound you make when you know the answer ('oh oh, I know!') while looking at a picture of a child waving his hand in the air. Students will practice o_e= /O/ by identifying what words have /O/ in them in both oral and written language and working with o_e= /O/ during a letter box lesson. It is important for children to know what sound every letter in the alphabet makes, so this will help clarify that the silent e makes o say its name. We will go over words that have /O/ in them, read a book with the o_e= /O/ correspondence in it, and practice listening for the /O/ sound so that children can reach the goal of knowing o_e= /O/. II. Materials: Is Jo Home? (need enough copies so each child in small group has one), flashcard with o_e= /O/ written on it, picture of child raising his hand, letterbox for each child, letters for each child (h, o, p, e, b, n, l, s, d, z, t, r, k), list of printed words, worksheet for each child 1. "Our way of reading is really hard to figure out, so today we're going to work on long vowel O. We have already learned short vowel o and that o= /o/ like in the word log. Long O sometimes has a special guide that we can use to help us read. When we see a silent e on the end of a word, like home, we know that e is telling us to say long vowel /O/. Let's look at this little boy raising his hand (show picture). Have you ever raised your hand and called out, 'Oh, Oh, I know the answer?!' Well this long vowel O, says Oh! So today we're going to be looking at words that are o_e=/O/ words (hold up flashcard with o_e= /O/ written on it). That silent e on the end makes long vowel o say its name." 2. "Look at the shape my mouth makes when I say /O/. It makes a little circle (show them your fingers going in circle around your mouth). When long vowel o is in words, our lips will make that small circle and you'll hear /O/. Let's practice. I want you to raise your hand and make that circle around your lips when you hear /O/ in a word. Do you hear /O/ in lap? Home? Broke? Sink? No?" 3. "Now I'm going to spell hope in our letter boxes. First watch me, then you'll have a turn to do it. I need to make sure I have a sound for every box so I'm going to slowly say my word. /Hhhh/, so I hear a h, so that goes in my first box. /Hhh/ /ooo/, I hear a o, so o goes in my second box. /Hhh/ /ooo/ /ppp/, I hear a /p/ so p goes in my third box. Since I can't hear that e on the end, it goes outside my third box. Remember, that silent e tells the o to say its name, /O/." 4. "Now it's your turn (each child in the small group will have letter box squares and letters). The first word is bone and you'll need three letter boxes. My dog likes to chew on bones. What sound do you hear first? (Walk around and make sure everyone is participating and spelling correctly?) What sound do you hear second? What sound do you hear last? Did everyone remember to put the silent e on the outside of the third box? Remember, that silent e makes o say its name /O/. Okay, the next word is pole (make sure everyone had the correct spelling of bone before moving on). The flag pole is silver. (Let children spell nose, stone, doze, hole, and stroke). (Walk around and monitor the children's work and make sure they are spelling each word correctly). Good work everyone!" 5. "Now I need you to read the words we just spelled (from list of printed words). First we're going to read them together, and then we're going to each read one. (Read list in unison, then call on each student to read a word)." 6. "Okay, now we're going to read a book called Is Jo Home? This book has lots of the o_e= /O/ spellings we've been working on! This book is about a dog who wants to play with Jo. The dog imagines all the fun things they can do together like eat ice cream and roll down a hill. But we don't know if Jo is home to play with the dog! You'll have to read the book to find out if the dog and Jo get to play together! First I want each of you to quietly read the book to yourself and I'm going to come by and get you to read a page to me out loud. (As children are reading quietly to themselves, I'm going to walk around and have each child read a page to me individually. Once I have assessed all of their reading, we'll go back to small group). Now we're going to read this book together!" (Read book out loud). 7. "Everyone did so awesome today! We're going to do this worksheet to review. These words are missing some letters. Fill in the o and silent e, and then color the pictures above the word you wrote! (Collect worksheet from children when done and assess their progress). Noie Yancey (2011), Oh, Oh, My Knee Hurts: Murray, G. (2004) Jakes joke. Reading Genie:

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To learn about volcanoes by making a volcano model. "Students should learn what causes earthquakes, volcanoes, and floods and how those events shape the surface of the earth. Students, however, may show more interest in the phenomena than in the role the phenomena play in sculpting the earth. So teachers should start with students’ immediate interest and work toward the science." (Benchmarks for Science Literacy p. 71.) For grades K-2, working with students’ immediate interests about the phenomena of erupting volcanoes is appropriate and probably the most meaningful way to introduce the topic of change. This lesson presents volcanoes through the making of volcano models. While students are constructing their physical representations of volcanoes, they will be filled with questions about volcanoes as well as how to build their models. This process will provide students with a tangible reference for learning about volcanoes and give them a chance to problem-solve as they build their models. Students will also be fascinated with the eruption aspect of volcanoes. In this lesson, students will be able to observe how the eruption changes the original form of their volcano model. In this way, students see first hand how this type of phenomenon creates physical change. While students at this level may struggle to understand larger and more abstract geographical concepts, they will work directly with material that will help them build a foundation for understanding concepts of phenomena that sculpt the earth. Many of the ideas in this lesson have been adapted from University of North Dakota's Volcano World website. To meet the needs and interests of your particular group of students, you can explore this site further to get additional creative ideas. It would be helpful to have a resource book available for students so they can refer to it themselves. It may also be helpful to prepare yourself by learning more about volcanoes. The following Web pages are good resources for your own background: It is suggested that you make your own volcano model in advance of doing this lesson with your students so that you can use your model to demonstrate an eruption. Most students have not seen a volcano first hand. Many students at the K-2 level may be unfamiliar with what volcanoes are. A good place to start is to show students a photograph of a volcano. For an online still photograph, students can go to Current Volcanic Activity. Or, if you have other pictures of volcanoes, make these available to students. After students have seen photographs, you can talk with them about how volcanoes have "hot liquid" inside of them (if your students are ready, you can tell them that this is called magma). Sometimes this magma comes out of the volcano really fast (when the magma comes out, it is called lava). When this happens, we say the volcano is erupting. Visit the Ring of Fire site with your students. This site shows a short film clip of an actual volcano erupting. To view the video, click on "Video Clip" near the top of the page. This visual and auditory depiction will help students form an idea of what we mean by volcanoes and eruption. Students will also have fun physically playing out the concept of eruption. Have them crouch down on the floor. Tell them that they are volcanoes. Inside they have hot liquid getting ready to come out. As the liquid begins to rise, their bodies begin to rise. Soon the lava comes out the top, very fast and strong. Have them act this out by standing and jumping up, with their hands extended to the sky, and making eruption sounds! Tell students that they will now have a chance to make their own volcanoes. Before they begin, lead a discussion about what they already know about volcanoes and the questions they may have. Some helpful questions to facilitate this discussion might be: - If you were to touch a volcano, what do you think it would feel like? - What sound do you think volcanoes make when they erupt? - What do you want to know about volcanoes? Go to Volcano Models to find many ideas for creating different types of volcanoes, including lists of necessary materials. You may want to choose a model that is appropriate for your group of students, or you can offer students the opportunity to vote on which model the class will make. Although the class as a whole will make more than one volcano, if everyone makes the same model, students will have more opportunities to compare and contrast as they work on this project. At this level, keeping the number of variables to a minimum is appropriate because it helps students focus on the questions you are posing. Have students work in small groups for this project. Working together will facilitate extended discussion about volcanoes. The students' questions and discussions with each other will help you know what kind of further information they are looking for about volcanoes, and their questions will shape the additional group discussions you will likely have in the classroom. Questions you might anticipate from students may be less about volcanoes themselves and more about how to make their models. This provides an excellent opportunity for problem-solving, both individually and among the group. Although the Building Volcano Models site suggests particular materials for making each volcano model, having other materials available for students supports their individual efforts to solve problems they may encounter while structuring their models. Once students have completed their volcanoes (but before they erupt), refer them to the Volcano 1 student sheet. Encourage students to draw pictures or write words that describe their volcanoes. To help them document their observations, you might ask them: - What does your volcano look like? - What shape does your volcano have? - What is the texture of its surface? - Does your volcano look the same from every angle, or does it look different when you turn it around? You can also provide students with string and ask them to measure their volcanoes, cutting the string to fit the size of their models. They can measure around the base of the volcanoes, as well as the height. You can ask, "When you measure your volcano with string, what do you find?" This will be a reference for them when they consider how their volcanoes may have changed after eruption. Now students will have fun watching their volcanoes erupt. (Some of the ideas listed on the site describe how to make the volcano erupt. If yours does not, the combination of baking soda and vinegar will give you an erupting effect.) Students may have difficulty thinking about particular observation questions during these eruptions because they will be so enthralled with the process of eruption. It is valuable for students to be involved with the eruptions in this way. Students will more easily be able to think critically about what they are seeing when they watch a volcano erupt a second time. So, if possible, videotape these eruptions or take before/after photographs. Then you can play the videotape of the eruptions (or show the before/after photos). Another alternative would be to create an eruption using a volcano that you made in advance. After watching their volcanoes erupt, you can ask students to look at the video/photos or watch yours erupt with particular questions in mind. For example: - Where is the "lava" coming out from? - Where is the lava going? - What do you hear as the lava is coming out? - Have you seen anything like this before? - What does it remind you of? Students have now been challenged, both during the process of constructing their models and in class discussions, to think about many aspects of volcanoes. Just as you asked them at the outset of this project, you can ask them again, "What do you want to know about volcanoes?" Be sure to answer as many of their questions as possible, as well as provide suggestions for how they can find their own answers. The Volcano 2 student sheet will give students a place to document the changes they have been able to observe. To help them think about these changes, ask: - What does your volcano look like now? - Is your volcano the same shape now that it has erupted? - Touch your volcano. Does it feel different? In what ways? - What made your volcano change? - When you use your measurement string, what do you find now? - Compare your volcano before it erupted to your volcano after it erupted. What is different? What has changed? Refer students to the Volcano 2 student sheet and ask them to draw or write about the kinds of questions you have just discussed. It will be helpful for them to have their volcanoes in front of them as they do this. To encourage students to consider how their models helped them learn about volcanoes, lead a discussion that includes the following questions: - How do you think your volcanoes are like real volcanoes? - How do you think they are different? - When you made your volcanoes, what helped you know what they looked like? - How could you have made your models better? In a simple discussion, you can also look at some of the recommended children's books with students to help them connect the idea of physical, geographical change. Just as their volcanoes changed after eruption, so too do real volcanoes. This causes some change on the earth's surface. Consider asking your students to write a story or poem about volcanoes. Or, students may enjoy putting their volcano ideas to music with either words or simply with instruments. Dramatic play opportunities are creative ways for students to communicate their new-found volcano knowledge. These ideas offer students ways to reflect upon what they have learned. By writing a story or creating volcano music, or whatever the choice may be, students are challenged to think about how the pieces of their volcano project fit together to make a whole picture. They are also challenged to document in a new way, as well as to communicate their learning to others. These are important and meaningful science processing skills. This is excellent experience for the students and gives you an idea of what they learned from doing this project. At the end of this lesson, students should be able to: - Describe their volcano models and how they made them. - Communicate their observations to another person. - Understand how their models changed after eruption. - Ask questions about volcanoes that indicate a higher level of understanding about them. Help students navigate Kids' Volcano Art Gallery. Here they will find volcano drawings done by other young students and have the option to submit their volcano drawing (from their student sheets) to this website. Students could also share their drawings with the rest of the class by giving a presentation or by helping to assemble a class volcano book. Students may enjoy submitting not only their volcano drawings, but also a poem or story they wrote, or the photographs you took of their project to the Volcano World website. Encourage students to create more volcano models with different materials. See Building Volcano Models for several ideas for constructing volcanoes. The following websites may be useful to you as you work with your particular group of students on ways to extend this project. Have fun!

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Dark matter is one of the central mysteries in astronomy. It’s estimated to comprise approximately 27% of the universe, but we can’t see it because it doesn’t emit light. In fact, scientists don’t have any direct evidence of the existence of dark matter, but they have circumstantial evidence—namely, the effects of its presence. Something with mass—presumably, dark matter—speeds up the orbits of stars around their galactic centers. Astronomers have also observed gravitational lensing or the bending of light due to the gravity of an object they can’t see. This phenomenon allowed the Hubble telescope to capture a “ring” of what researchers believe is dark matter back in 2007. Artist rendering of Earth surrounded by hairy dark matter. Credit: NASA/JPL-Caltech Thus, scientists have for decades postulated the widespread existence of invisible matter or “missing mass.” A few years ago, NASA found more evidence in the discovery of 400,000 positrons thought to be the remains of dark matter collisions. Suffice it to say that astronomers are constantly on the lookout for direct or indirect evidence of dark matter. To do this, scientists look to the past, or at light that has traveled millions of light years to become visible to their equipment. Recently, the Max Planck Institute for Extraterrestrial Physics and researchers from around the globe studied six galaxies that formed roughly 10 billion years ago. They thought they would find indications of the central role of dark matter, but they didn’t. Ring of Dark Matter around galaxy cluster CL 0024+17. Credit: NASA/ESA Instead, researchers found that these galaxies are “strongly dominated by normal matter.” Normal matter, also called baryonic matter, is the stuff we can see, such as gas, dust, and stars. They also found that the rotation velocities of these galaxies decrease farther away from their centers—but dark matter is thought to either speed up a galaxy’s rotational velocity as the radius increases or at least keep it constant. Observations of another 200 galaxies also indicate higher levels of baryonic matter than anticipated, particularly in the form of gas, suggesting that dark matter perhaps plays a less crucial role in nascent galaxies than previously thought. Collage of six cluster collisions with dark matter maps. Credit: NASA/ESA Scientists believe that the gas in these early galaxies condensed into what they call “dark matter halos,” but that the dark matter within those halos didn’t condense until much later. This timeline would explain why dark matter doesn’t seem to exert much of an influence over the rotational velocities of early galaxies and why “present-day spirals, such as our Milky Way, require additional dark matter in various amounts,” according to study author Natascha Förster Schreiber. Cosmos 3D Dark Matter Map. Credit: NASA/ESA/Richard Massey (California Institute of Technology) While initially surprising, these findings make sense given what astronomers know about the formation of galaxies and the role they believe dark matter plays. Perhaps now that they know more about the relationship between timing and dark matter condensation, scientists will have better ideas about where and how to search for direct evidence of this elusive material.

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In a previous chapter of study, the variety of ways by which motion can be described (words, graphs, diagrams, numbers, etc.) was discussed. In this unit (Newton's Laws of Motion), the ways in which motion can be explained will be discussed. Isaac Newton (a 17th century scientist) put forth a variety of laws that explain why objects move (or don't move) as they do. These three laws have become known as Newton's three laws of motion. The focus of Lesson 1 is Newton's first law of motion - sometimes referred to as the law of inertia. Newton's first law of motion is often stated as An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. Two Clauses and a Condition There are two clauses or parts to this statement - one that predicts the behavior of stationary objects and the other that predicts the behavior of moving objects. The two parts are summarized in the following diagram. The behavior of all objects can be described by saying that objects tend to "keep on doing what they're doing" (unless acted upon by an unbalanced force). If at rest, they will continue in this same state of rest. If in motion with an eastward velocity of 5 m/s, they will continue in this same state of motion (5 m/s, East). If in motion with a leftward velocity of 2 m/s, they will continue in this same state of motion (2 m/s, left). The state of motion of an object is maintained as long as the object is not acted upon by an unbalanced force. All objects resist changes in their state of motion - they tend to "keep on doing what they're doing." There is an important condition that must be met in order for the first law to be applicable to any given motion. The condition is described by the phrase "... unless acted upon by an unbalanced force." As the long as the forces are not unbalanced - that is, as long as the forces are balanced - the first law of motion applies. This concept of a balanced versus and unbalanced force will be discussed in more detail later in Lesson 1. Suppose that you filled a baking dish to the rim with water and walked around an oval track making an attempt to complete a lap in the least amount of time. The water would have a tendency to spill from the container during specific locations on the track. In general the water spilled when: - the container was at rest and you attempted to move it - the container was in motion and you attempted to stop it - the container was moving in one direction and you attempted to change its direction. The water spills whenever the state of motion of the container is changed. The water resisted this change in its own state of motion. The water tended to "keep on doing what it was doing." The container was moved from rest to a high speed at the starting line; the water remained at rest and spilled onto the table. The container was stopped near the finish line; the water kept moving and spilled over container's leading edge. The container was forced to move in a different direction to make it around a curve; the water kept moving in the same direction and spilled over its edge. The behavior of the water during the lap around the track can be explained by Newton's first law of motion. Everyday Applications of Newton's First Law There are many applications of Newton's first law of motion. Consider some of your experiences in an automobile. Have you ever observed the behavior of coffee in a coffee cup filled to the rim while starting a car from rest or while bringing a car to rest from a state of motion? Coffee "keeps on doing what it is doing." When you accelerate a car from rest, the road provides an unbalanced force on the spinning wheels to push the car forward; yet the coffee (that was at rest) wants to stay at rest. While the car accelerates forward, the coffee remains in the same position; subsequently, the car accelerates out from under the coffee and the coffee spills in your lap. On the other hand, when braking from a state of motion the coffee continues forward with the same speed and in the same direction, ultimately hitting the windshield or the dash. Coffee in motion stays in motion. Have you ever experienced inertia (resisting changes in your state of motion) in an automobile while it is braking to a stop? The force of the road on the locked wheels provides the unbalanced force to change the car's state of motion, yet there is no unbalanced force to change your own state of motion. Thus, you continue in motion, sliding along the seat in forward motion. A person in motion stays in motion with the same speed and in the same direction ... unless acted upon by the unbalanced force of a seat belt. Yes! Seat belts are used to provide safety for passengers whose motion is governed by Newton's laws. The seat belt provides the unbalanced force that brings you from a state of motion to a state of rest. Perhaps you could speculate what would occur when no seat belt is used. There are many more applications of Newton's first law of motion. Several applications are listed below. Perhaps you could think about the law of inertia and provide explanations for each application. - Blood rushes from your head to your feet while quickly stopping when riding on a descending elevator. - The head of a hammer can be tightened onto the wooden handle by banging the bottom of the handle against a hard surface. - A brick is painlessly broken over the hand of a physics teacher by slamming it with a hammer. (CAUTION: do not attempt this at home!) - To dislodge ketchup from the bottom of a ketchup bottle, it is often turned upside down and thrusted downward at high speeds and then abruptly halted. - Headrests are placed in cars to prevent whiplash injuries during rear-end collisions. - While riding a skateboard (or wagon or bicycle), you fly forward off the board when hitting a curb or rock or other object that abruptly halts the motion of the skateboard. Try This At Home Acquire a metal coat hanger for which you have permission to destroy. Pull the coat hanger apart. Using duct tape, attach two tennis balls to opposite ends of the coat hanger as shown in the diagram at the right. Bend the hanger so that there is a flat part that balances on the head of a person. The ends of the hanger with the tennis balls should hang low (below the balancing point). Place the hanger on your head and balance it. Then quickly spin in a circle. What do the tennis balls do?

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Bubble Sorting Algorithm The bubble sorting method is one of the most basic types of algorithms implemented to accurately place items in either ascending or descending order. According to Astrachan (2003), the algorithm was first introduced in 1959 by the name ‘exchange sort.’ For unknown reasons, a few years later (1962) a computer scientist published a journal article in which he changed the name from ‘exchange sort,’ to ‘bubble sort.’ Throughout the next few decades, many synonyms to the algorithm have been proposed (i.e., ‘sorting by repeated comparisons and exchanging,’ ‘shuttle sort’), however most computer scientists today still use the term bubble sort (Astrachan, 2003). Bubble sorting is one of the most basic types of sorting methods. The method consists of looking at the first two items (generally starting at the left side) that are next to each other, and switching them if they are in the wrong order relative to an ascending or descending pattern. After the two items have been switched if in the wrong order, or left untouched if in the correct order, the procedure shifts one number to the right and repeats until the entire list has been sorted. The following is an example of the bubble sorting method sorting the numbers in ascending order; given the numbers, 5, 9, 2, 0, 1: Step 1. 5, 9, 2, 0, 1 The numbers 5 and 9 are compared. Because the number 5 is less than the number 9, the numbers do not switch. Step 2. 5, 2, 9, 0, 1 The numbers 9 and 2 are compared. Because the number 9 is greater than the number 2, the numbers switch. Step 3. 5, 2, 0, 9, 1 The numbers 9 and 0 are compared. Because the number 0 is less than the number 9, the numbers switch. Step 4. 5, 2, 0, 1, 9 The numbers 1 and 9 are compared. Because the number 1 is less than 9, the numbers switch. At this point we now have 5, 2, 0, 1, 9. Because the highest number is now in the correct position, it can be ignored and the other numbers can be swapped using the same technique until all of the numbers fall in ascending order. The bubble sorting method can be written as О(n2), in which n represents the total number of items being sorted, whereas O represents how running time grows as n grows. Because n is squared, which significantly increases running time, bubble sorting is not efficient when dealing with a larger number of items (Hillis, 2015). Furthermore, the bubble sorting method is inefficient if the numbers are in the worst-case scenario (i.e., all the largest numbers are on the left side when sorting in ascending order from left to right), as the method would require numerous steps before all of the items are placed in the correct order. To combat these issues, a number of other algorithms are more efficient and produce the same results. One algorithm, known as the merge sorting, involves a recursion method (Hillis, 2015). The merging method involves dividing the total number of items in half and sorting those two halves in ascending order. Next, combine the two halves back together by successively taking the lowest numbered item on top of the stack and placing it in order. The merge sorting method can be written as n log n. Using the example we used with the bubble sorting method (i.e., using the number 5, 9, 2, 0, 1), here is how the merge sorting method would work: Step 1. Divide 5, 9, 2 into one stack, and 0, 1 into another stack Step 2. Assort 5, 9, 2, into ascending order (i.e., 2, 5, 9) Step 3. Compare the top card of the two stacks. 0 would be compared to 2, so zero would be placed first as it is a lower number. Additionally, 1 is also smaller than 2, so 1 would be placed before 2, which would then be followed by 2, 5, and 9. As displayed, the bubble method can be easily done manually. Due to the amount of time it takes to put a large number of items in order, and due to the possibility of the worst-case scenario, this algorithm is rarely used in programming. However, the bubble method is occasionally implemented when fixing minute computer graphics that can be adjusted with using only linear complexity (Bubble Sort, 2017). What makes bubble sorting special and unique is its simplicity. Although it may not be the best and most efficient algorithm to use, it is an ideal technique to teach when introducing algorithms to students who have no background in computer science (e.g., the author of this paper). Many computer scientists have ridiculed teaching this method due to its potential misuse (i.e., using it when n is a large value; Astrachan, 2003); however if taught the drawbacks to the method, it can be the initial stepping-stone to delving into the world of algorithms and heuristics. Switching to a first person perspective, on a personal note, I think the bubble sorting method is useful in teaching the basics to algorithms and heuristics to individuals who have no experience in computer science. Before reading the chapter, I didn’t know what an algorithm even was. However, because Hillis started as simple as possible (and used the sock analogy), I quickly learned their use. As Hillis described, and as we practiced in class, the bubble method was my first step in learning about algorithms. Prior to writing about the bubble sorting method (perhaps the most simple algorithm out there), I was going to write about an algorithm that found variance. Because I run many ANOVAs on my cognitive psychology research team, I thought it would be very interesting to see how the programs I use (i.e., SPSS, JMP, MATLAB) can analyze variance and regression analyses. After failing to interpret any of the equations, I decided to give up on the topic and go for something more basic. However, what I did learn was that before these computer programs were developed, the job of a psychologists and a mathematician was very similar. Hopefully, once I complete more statistics, I will be able to understand and comprehend algorithms that are more complex than the bubble sorting method. Astrachan, O. (2003). Bubble sort: An archaeological algorithmic analysis (Doctoral Dissertation). Retrieved from https://users.cs.duke.edu/~ola/papers/bubble.pdf Bubble Sorting Method. (n.d.). In Wikipedia. Retrieved February 7, 2017, from https://en.wikipedia.org/wiki/Bubble_sort Hillis, D. W. (2015). The pattern on the stone: The simple ideas that make computers work. New York, NY: Basic Books.

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In this probability worksheet, 6th graders solve 4 problems. They toss coins, imagine spinners and create a probability experiment that involves tossing coins. 3 Views 9 Downloads Theoretical Probability Activity If you keep rolling a die, you'll roll a five exactly one-sixth of the time—right? A probability lesson prompts young mathematicians to roll a die 100 times and use the data to calculate empirical probabilities. They then compare these... 6th - 8th Math CCSS: Designed Activity: An Experiment with Dice Roll the dice with this activity and teach young mathematicians about probability. Record outcomes for rolling two number cubes in order to determine what is most likely to happen. Graph the data and investigate patterns in the results,... 3rd - 7th Math CCSS: Adaptable Find the Experimental Probability by Creating a Ratio Check out a great visual introduction to probability and how to write a ratio expressing the outcomes. The video first reviews how to find the probability and the difference between theoretical and experimental. Use the classic dice... 4 mins 6th - 8th Math CCSS: Designed Understand the Law of Large Numbers by Comparing Experimental Results to the Theoretical Probability If we flip four tails in a row, does that mean all coin flips will be tails? With the law of large numbers, your mathematicians will learn that with more trials their experimental probability will get closer to the theoretical... 5 mins 6th - 8th Math CCSS: Designed

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In functional programming, referential transparency is generally defined as the fact that an expression, in a program, may be replaced by its value (or anything having the same value) without changing the result of the program. This implies that methods should always return the same value for a given argument, without having any other effect. This functional programming concept also applies to imperative programming, though, and can help you make your code clearer. To understand this article you should know how to write simple classes and methods in Java. Knowing what a side effect is helps but if you don't, you'll learn it on the way. The expression referential transparency is used in various domains, such as mathematics, logic, linguistics, philosophy and programming. It has quite different meanings in each of these domain. Here, we will deal only with computer programs, although we will show analogy with maths (simple maths, don't worry). Note, however, that computer scientists do not agree on the meaning of referential transparency in programming. What we will look at is referential transparency as it is used by functional programmers. Referential Transparency in Maths In maths, referential transparency is the property of expressions that can be replaced by other expressions having the same value without changing the result in any way. Consider the following example: x = 2 + (3 * 4) We may replace the subexpression (3 * 4) with any other expression having the same value without changing the result (the value of x). The most evident expression to use, is of course 12: x = 2 + 12 Any other expression having the value 12 (maybe (5 + 7)) could be used without changing the result. As a consequence, the subexpression (3 * 4) is referentially transparent. We may also replace the expression 2 + 12 by another expression having the same value without changing the value of x, so it is referentially transparent too: x = 14 You can easily see the benefit of referential transparency: It allows reasoning. Without it, we could not resolve any expression without considering some other elements. Continue reading \%What Is Referential Transparency?\%

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In this Section: In this section, we learn how to algebraically manipulate a linear equation in two variables into different forms. We start by officially learning about slope-intercept form. This form of a line: y = mx + b, allows us to easily identify the slope as: ‘m’ and the y-intercept as: ‘(0,b)’. There are many different uses for this form of a line. As we have previously seen, it is much easier to graph a linear equation in this format. Next, we turn to point-slope form. This form of the line is used when we know one point and the slope, or two points on the line. Point-slope form: y - y1 = m(x - x1). We can plug in our known point and the slope and solve for y to place the equation in slope-intercept form. We conclude our lesson by learning about standard form. This form of the line carries different definitions, based on the text. In most high school courses, the form is given as: ax + by = c, where a, b, and c are integers, a ≥ 0, a and b are not both zero, and a, b, and c share no common factor other than 1. Most higher level math courses are less strict on this definition. We have the format of: ax + by = c, where a, b, and c are real numbers and a and b are not both zero.

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The auditory system is divided into three distictive parts. The outer ear, middle ear and inner ear. In the process of hearing, each division has a distinct and specific function. The mechanism of hearing involves the transmission of vibrations, the generation of nerve impulses, and sound recognition in the brain. The following graphic shows the basic areas of the ear. The sense of hearing involves mechanical action as sound waves enter the external auditory meatus, where they are transformed into impulses. As the impulses pass through the external auditory canal, they impinge on the tympanic membrane. Energy from the sound waves cause the tympanic membrane to vibrate. These vibrations are transferred directly to the middle ear bones, called ossicles, causing them to vibrate in a chain reaction. The first ossicle, known as the malleus, is attached to the tympanic membrane. As the vibrations hit the tympanic membrane the malleus vibrates causing the the second ossicle, the incus, to vibrate. The generated vibrations cause the innermost ossicle, the stapes to vibrate. The foot plate of the stapes fits into the oval window, a small opening in the wall between the middle and inner ear. This lever like system amplifies the sound waves as the vibrations move through the middle ear into the inner ear. The vibrations are now passed into the fluid of the inner ear into the cochlea. The cochlear duct which is located just inside the cochlea, houses the Organ of Corti. The Organ of Corti contains the auditory receptor cells/hair cells, supporting cells and nerve fibers. The receptor cells are embedded in the basilar membrane of the cochlear duct. A gelatinous membrane called the tectorial membrane overhangs and touches the haircells of the basilar membrane. Fluid movement caused by the sound waves entering the cochlea leads to movement of the basilar membrane. This causes the thousands of hair cells covering it to excite the receptor nerve endings and send an electrical signal through the auditory nerve to the temporal lobe of the brain. The brain decodes the impulses and recognizes them as sound.

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This word problem resource is designed to save time and paper, while helping students to solve word problems directly into their math notebooks. Students glue in multiple word problems (in small boxes to save on space) and solve into journal with drawing, number sentences, etc. Word problems are differentiated to meet the needs of your students, so please utilize! Covers addition, subtraction, measurement and money!! This resource covers the following skills: 2.NBT.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. 1.MD.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object. 2.MD.4/5 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. 2.MD.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. -Subtraction: Subtraction word problems - one-digit numbers -Subtraction: Word problems - write the subtraction sentence -Subtraction: Subtraction word problems - numbers up to 18 -Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions. -Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions. -Subtraction - one digit: Subtraction word problems - up to 18 -Addition - two digits: Addition word problems - up to two digits -Subtraction - two digits: Subtraction word problems - up to two digits -Mixed operations: Addition and subtraction word problems - up to 20 -Mixed operations: Addition and subtraction word problems - up to 100 Please contact me with any questions!

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RL.6: Craft and Structure Anchor Standard CCRA.R.6 Assess how point of view or purpose shapes the content and style of a text. 11th-12th Grades RL.11-12.6 Analyze a case in which grasping a point of view requires distinguishing what is directly stated in a text from what is really meant (e.g., satire, sarcasm, irony, or understatement). 9th-10th Grades RL.9-10.6 Analyze a particular point of view or cultural experience reflected in a work of literature from outside the United States, drawing on a wide reading of world literature. 8th Grade RL.8.6 Analyze how differences in the points of view of the characters and the audience or reader (e.g., created through the use of dramatic irony) create such effects as suspense or humor. 7th Grade RL.7.6 Analyze how an author develops and contrasts the points of view of different characters or narrators in a text. 6th Grade RL.6.6 Explain how an author develops the point of view of the narrator or speaker in a text. 5th Grade RL.5.6 Describe how a narrator’s or speaker’s point of view influences how events are described. 4th Grade RL.4.6 Compare and contrast the point of view from which different stories are narrated, including the difference between first- and third-person narrations. 3rd Grade RL.3.6 Distinguish their own point of view from that of the narrator or those of the characters. 2nd Grade RL.2.6 Acknowledge differences in the points of view of characters, including by speaking in a different voice for each character when reading dialogue aloud. 1st Grade RL.1.6 Identify who is telling the story at various points in a text. Kindergarten RL.K.6 With prompting and support, name the author and illustrator of a story and define the role of each in telling the story. Anchor Notes To build a foundation for college and career readiness, students must read widely and deeply from among a broad range of high-quality, increasingly challenging literary and informational texts. Through extensive reading of stories, dramas, poems, and myths from diverse cultures and different time periods, students gain literary and cultural knowledge as well as familiarity with various text structures and elements. By reading texts in history/social studies, science, and other disciplines, students build a foundation of knowledge in these fields that will also give them the background to be better readers in all content areas. Students can only gain this foundation when the curriculum is intentionally and coherently structured to develop rich content knowledge within and across grades. Students also acquire the habits of reading independently and closely, which are essential to their future success.

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The Constitution provides a federal system of government in the country even though it describes India as ‘a Union of States’. The term implies that firstly, the Indian federation is not the result of an agreement between independent units, and secondly, the units of Indian federation cannot leave the federation. The Indian Constitution contains both federal and non- federal features. The federal features of the Constitution include: (1) A written constitution which defines the structure, organization and powers of the central as well as state governments (2) A rigid constitution which can be amended only with the consent of the states (3) An independent judiciary which acts as the guardian of the constitution. (4) A clear division of powers between the Center and the States through three lists- Union list, State list and Concurrent list (5) The creation of an Upper House (Rajya Sabha) which gives representation to the states, etc. Non – Federal Features The Constitution also contains a number of unitary features: (1) The creation of a very strong centre (2) The absence of separate constitutions for the states (3) The right of Parliament to amend major portions of the constitution by itself (4) A single citizenship for all (5) Unequal representation to the states in the Rajya Sabha (6) The right of Parliament to change the name, territory or boundary of states without their consent (7) The presence of All- India Services which hold key positions in the Centre as well as the States appointment of the Governor by the President (8) The granting of extensive powers to the President to deal with various kinds of emergencies (9) The right of Parliament to legislate on state subjects on the recommendation of the Rajya Sabha (10) The presence of a single judiciary with the Supreme Court of India at the apex (11) The residuary powers under the Indian Constitution are assigned to the Union and not to the States. (12) The exclusive right of Parliament to propose amendments to the Constitution. (13) On account of the presence of a large number of non- federal features in the Indian Constitution India is often described as a ‘quasi-federal ‘country. CENTRE – STATE RELATIONS Relations between the Union and States can be studied under the following heads (a) Legislative Relations- The Constitution divides legislative authority between the Union and the States in three lists- the Union List, the State List and the Concurrent List. The Union list consists of 99 items. The Union Parliament has exclusive authority to frame laws on subjects enumerated in the list. These include foreign affairs, defence, armed forces, communications, posts and telegraph, foreign trade etc. The State list consists if 61 subjects on which ordinarily the States alone can make laws. These include public order, police, administration of justice, prison, local governments, agriculture etc. The Concurrent list comprises of 52 items including criminal and civil procedure, marriage and divorce, economic and special planning trade unions, electricity, newspapers, books, education, population control and family planning etc. Both the Parliament and the State legislatures can make laws on subjects given in the Concurrent list, but the Centre has a prior and supreme claim to legislate on current subjects. In case of conflict between the law of the State and Union law on a subject in the Concurrent list, the law of the Parliament prevails. Residuary powers rest with the Union government. Parliament can also legislate on subjects in the State list if the Rajya Sabha passes a resolution by two-third majority that it is necessary to do so in the national interest. During times of emergency, Parliament can make laws on subjects in the State List. Under Article 356 relating to the failure of constitutional machinery in the state, Parliament can take over the legislative authority of the state. Likewise, for the implementation of international treaties or agreements, Parliament can legislate on state subjects. Finally, Parliament can make laws on subjects in the State list if two or more states make a joint request to it to do so. Thus, the Centre enjoys more extensive powers than the states. (b) Administrative relations- The Indian Constitution is based on the principle that the executive power is co-extensive with legislative power, which means that the Union executive/the state executive can deal with all matters on which Parliament/state legislature can legislate. The executive power over subjects in the Concurrent list is also exercised by the states unless the Union government decides to do so. The Centre can issue directives to the state to ensure compliance with the laws made by Parliament for construction and maintenance of the means of communications declared to be of national or military importance, on the measures to be adopted for protection of the railways, for the welfare of the scheduled tribes and for providing facilities for instruction in mother tongue at primary stage to linguistic minorities. The Centre acquires control over states through All India Services, grants- in- aid and the fact that the Parliament can alone adjudicate in inter- state river disputes. During a proclamation of national emergency as well as emergency due to the failure of constitutional machinery in a state the Union government assumes all the executive powers of the state. (c) Financial Relations – Both the Union government and the states have been provided with independent sources of revenue by the Constitution. Parliament can levy taxes on the subjects included in the Union list. The states can levy taxes on the subjects in the state list. Ordinarily, there are no taxes on the subjects in the Concurrent List. In the financial sphere also the States are greatly dependent on the Centre for finances. The Centre can exercise control over state finances through the Comptroller and Auditor General of India and grants. but during financial emergency the President has the power to suspend the provision regarding division of taxes between the centre and the states. Finance Commission –One of the instruments which the Constitution has evolved for the purpose of distributing financial resources between the Centre and the states is the Finance Commission. The Finance Commission according to Article 280 of the Constitution is constituted by the President once every five year and is a high- power body. The duty of the Commission is to make recommendations to the President as to: (a) the distribution between the union and the states of the net proceeds of the taxes which are to be divided between them and the allocation between the states themselves of the respective share of such proceeds; (b) the principles which should govern the grants-in-aid of the revenues amongst the states out of the Consolidated Fund of India. Co- operative Federalism The Indian Constitution provides for a number of mechanisms to promote co-operative federalism. Article 263 empowers the President to establish Inter-State Council to promote better co-ordination between the Centre and States. Inter -State Council was formally constituted in 1990. It is headed by the Prime Minister and includes six Cabinet ministers of the Union and Chief Ministers of all the states and union territories. Zonal Councils were set up under the State Re-organization Act, 1956, to ensure greater cooperation amongst states in the field of planning and other matters of national importance. The act divided the country into six zones and provided a Zonal Council in each zone. Each council consists of the Chief Minister and two other ministers of each of the states in the zone and the administrator in the case of the union territory. The Union Home Minister has been nominated to be the common chairman of all the zonal councils. Next Topic: Union Territories and Jammu and Kashmir Previous Topic: The State Legislature

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Creating your own color-by-number worksheets for the classroom is an easy task that allows you to reinforce educational concepts in a creative way. For instance, instead of using a simple color key, you could incorporate math concepts such as even and odd, two- or three-digit numbers or even specific facts (all facts totaling 5, for example) to indicate which colors to use in certain areas. For a language-arts worksheet, you could incorporate synonyms and antonyms into the color key. Student color-by-number papers can teach a lesson while also serving as a quiet classroom activity. Choose a graphic for the coloring sheet. You can copy a coloring book page or download a black and white image from the Internet. If you are creative, you could draw your own image. Print out the image from a computer or use a copy machine to make a master copy of the worksheet. If standard-size copy paper does not give you enough room to write instructions for the students, use a larger size, such as legal-size paper. If legal-size paper is not available, you can print the color key information and any other instructions on a separate sheet of paper. Write the color key information on the bottom of the page to guide the students. The color key should be simple and easy to understand. For example, you could say, "Even-numbered spaces -- color blue" or "Synonyms of the word 'pretty' -- color green." Use a dark permanent marker to write the numbers or words designated in the color key on the master copy. Make a copy of the worksheet for each student. Things You Will Need - Coloring book or downloaded image - Copy paper - Copy machine or computer printer - Permanent marker - Jupiterimages/Comstock/Getty Images

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You've gone through a unit on motion; your students know the difference between velocity and acceleration. (Or, at least some of them do, some of the time.) Now you're ready to introduce F = ma. What do you do first? I think most physics teachers, and certainly most textbooks, recognize the necessity of diving into free body diagrams right away. Somehow, you must show the difference between an individual force and the NET force. I concentrate on getting students to write out the object applying and experiencing the force; this helps avoid including fictitious forces (like "force of motion"), and it makes a future discussion of the third law child's play. But, what do you do with those free body diagrams, other than make them? (1) Some books and teachers jump to a mathamatical treatment of F = ma. Practice problems in which the free body is used to determine the value of the net force, use the second law to determine acceleration, then use kinematics to get something like the initial or final speed of an object, or its time in motion. Then you can do the reverse -- use motion information to calculate net force, and then the amount of an individual force. (2) Others go from the free body diagram to a semi-quantitative treatment of F = ma. That is, show mathematically and experimentally that at constant mass, a larger net force yields a larger acceleration; for constant acceleration, a larger mass demands a larger net force. Linear graphs can be created to verify the second law relationship. While I get to both (1) and (2), I don't start there. I start merely with free body diagrams and the direction of motion. But Greg, you say. Free body diagrams have nothing to do with the direction of motion. Yes. That's the point. Before I do any work with the relationship F = ma, I ask every possible question I can think of about how the object is moving. Here we're considering motion in a line only; circular and projectile motion are for later on. For example: This cart experiences a 3 N force to the left, and a 2 N force to the right. * Which way is the net force on the cart? (Left, because the greater forces act to the left.) * Which way is the cart's acceleration? (Left, because net force is always in the direction of acceleration, and we just said net force acts left.) * Which way is the cart moving? (No clue. Acceleration and motion aren't simply related. The cart could be moving left and speeding up, or moving right and slowing down.) * Could the cart be moving to the right? (Sure -- if the cart is slowing down. Note that the most common answer which is utterly unacceptable is "Yes, if another object applied another 2 N force to the right.") * Could the cart be moving left at 1 m/s? (Sure, as long as its speed a moment later is greater than 1 m/s. NOT "Yes, as long as its mass is 1 kg.") * Could the cart be moving left at a constant speed of 1 m/s? (No way. The cart experiences a net force, so the cart has an acceleration, so the cart's speed must change.) It's useful to let students play with the phet simulation "force and motion basics." In class, I have students do a series of experiments in which they predict the force necessary to cause an object to speed up or slow down. We don't worry about the actual value of acceleration, just the directions of motion and acceleration. Once my students are rolling their eyes at these sorts of questions, answering with the same voice that my son uses when I remind him to wear a jacket to school on a cold day... well, then you're ready to move on to lessons (1) and (2) above.

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The experimental discovery that almost all chemical reactions either absorb or release heat led to the idea that all substances contain heat. Consequently, the heat of a reaction is the difference in the heat contents of the products and reactants: Δ H = H products – H reactants Throughout this book, the Greek letter delta Δ will be used to symbolize change. Chemists use the term enthalpy for the heat content of a substance or the heat of a reaction, so the H in the previous equation means enthalpy. The equation states that the change in enthalpy during a reaction equals the enthalpy of the products minus the enthalpy of the reactants. You can consider enthalpy to be chemical energy that is commonly manifested as heat. Use the decomposition of ammonium nitrate as an example of an enthalpy calculation. The reaction is and the enthalpies of the three compounds are given in Table 1. Notice that the enthalpies can be either positive or negative. In general, compounds that release heat when they are formed from their elements have a negative enthalpy, and substances that require heat for their formation have a positive enthalpy. The enthalpy of the decomposition reaction can be calculated as follows: Observe the doubling of the enthalpy of H 2O (–36 kJ/mole) because this compound has a stoichiometric coefficient of 2 in the reaction. The overall enthalpy of the reaction is –36 kilojoules, which means that the decomposition of 1 mole of ammonium nitrate releases 36 kJ of heat. The release of heat means that this is an exothermic reaction. The sign of the enthalpy of the reaction reveals the direction of heat flow. See Table 2. If you reverse the previous reaction, the sign of the enthalpy of the reaction is reversed: Δ H = +36 kJ The reversed reaction is, therefore, endothermic. It would require the addition of 36 kcal of energy in order to cause the nitrous oxide and water vapor to react to form 1 mole of ammonium nitrate. The calculations on the ammonium nitrate reaction demonstrate the immense value of tables that list the enthalpies for various substances. The values at 25°C and 1 atm are called standard enthalpies. For elements, the standard enthalpy is defined as 0. For compounds, the values are called standard enthalpies of formation because the compounds are considered to be formed from elements in their standard state. Table 3 gives a few values that will be used in subsequent examples and problems. The symbol for standard enthalpies of formation is , where the superscript denotes standard and the subscript denotes formation. Look up both elemental sulfur and nitrogen to see that the standard enthalpies for elements are 0. Then find the pairs of values for H 2O and CCl 4 (carbon tetrachloride) to learn that the enthalpy depends on the state of matter. Use the data in Table 3 to calculate the enthalpy change of the following reaction: The difference in the heats of formation of the products is given by: The enthalpy of the reaction is –1124 kilojoules, meaning that the oxidation of 2 moles of hydrogen sulfide yields or releases 1124 kJ of heat. This reaction is exothermic. Use Table 3 for the next two problems. - Calculate the enthalpy change for the following reaction and classify it as exothermic or endothermic. - Calculate the quantity of heat released when 100 grams of calcium oxide react with liquid water to form Ca(OH) 2 ( s).

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There are three main properties that make electricity work: voltage, current and resistance. These properties work together inside a circuit, allowing electricity to move from place to place. Scientists measure voltage in units called volts, current in amps, and resistance in ohms. These three quantities lead to a simple mathematical relation called Ohm's Law, where a voltage of one volt across a resistance of one ohm gives a current of one amp. Movement Of Electrons The process of electricity begins when energy from light, heat, or magnetic fields stimulates an atom's electrons, making them move. Some atoms hold their electrons close to the nucleus and some don't. The atoms with a loose hold on their electrons are best at conducting an electrical current. Conductors And Insulators Materials such as silver, gold, copper and aluminum have atoms with loosely-bound electrons, these elements are all metals, and most metals are good conductors of electricity. Materials like glass, air and plastic are called insulators; their electron makeup obstructs the flow of an electric current. Current And Voltage In order for electricity to flow in a current, there must be some sort of force or pressure pushing the electrons along. This force is called electromotive force or EMF, which is also called voltage. Parts Of An Electrical Circuit A circuit carries this electrical current. It is comprised of an electrical source, a load and conductors such as wires that carry the current between the source and the load. An example of an electrical source is a battery. The load could be nearly any kind of electronic component, from a simple light bulb to complex devices such as smartphones. Voltage And Current The amount of electromotive force applied by the source determines how much voltage goes through the circuit. By contrast, current is the quantity of electrons that flow past a point in the circuit in a given amount of time. The last piece of the electricity puzzle has to do with the kind of resistance that is working against the electrical current. For example, if you were to use two heavy-gauge wires in your circuit, more current would flow than if you were to use two thin wires. The thicker wires have less resistance and permit a greater current. It is similar to water flowing through a pipe: A large pipe can carry more water than a narrow one. Electricity And Power Electricity carries power, and you can calculate electrical power in watts by multiplying volts by amps. Current flows from the electrical source to the load and back again; the load uses the electrical power to accomplish a useful task, such as lighting a kitchen lamp or running an electric motor in a hybrid car.

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Why are the Andes so tall? Plate-tectonics study could explain why some mountains are higher than expected. A three-dimensional model of our planet's plate tectonics could help to explain why the Andes mountain range is taller than geologists would predict: it could all be down to the long length of the South American continent. The highest mountain range on our planet — the Himalayas — was formed by the massive collision of two continental plates. But the Andes were formed where an oceanic plate slides beneath a continent. While this 'subduction' process is expected to create mountains through a crumpling of the continental plate above, it's perplexing why the peaks of the central Andes stand at an average height of 4 kilometres. Previous calculations based on models of plate tectonics have at times suggested they ought to be half that height. To investigate, Wouter Schellart of the Australian National University in Canberra and colleagues created a computer model of the motion of Earth's tectonic plates over millions of years. They plugged in values for the strength and density of our planet's different plates, allowed gravity to pull the denser ones down, and watched what happened. The team was particularly interested in what would happen to the shape of the boundary line between the subducting plate and the overriding one (called the subduction zone) — as seen from a bird's eye view. When subduction zones are short from tip to tail they move relatively quickly, the team found, rapidly adopting a 'U' shape as seen from above. But longer boundaries — such as the subduction zone off the South American coast, which measures 7,400 kilometres from north to south — move more slowly and develop into a 'W' shape. Sneaking round the edge The boundary of a sinking plate is known to generally retreat backwards as more and more material slides underground. For example, the South American subduction zone, in which the subducting plate is moving eastwards, tries to move westwards over time. This leaves a gap on the side of the overriding plate that needs to be filled in with rock. The upper-mantle material beneath the subducting plate steps in to fill that gap, flowing around the edges of the sinking plate to get there. When the length of the subduction zone is just a few hundred kilometres long, this flow of replacement rock is easy, the model shows. It simply nips around the edges, bending them as it does so. The result is a 'U'-shaped subduction zone. But with long boundaries, it is too difficult for mantle rock from the middle of the subducting plate to travel all the way around that plate's edges to fill in a gap on the other side, the model finds. For South America, this means that the subduction zone bends at the northern and southern ends, as expected. But in the middle — near Bolivia — the boundary doesn't move much at all. Make me a mountain Because the overriding plate of South America is moving westward at some 2 centimetres per year, this causes a serious crunch at the middle of the subduction zone. Over the past 30 million years or so, says Schellart, 300-350 kilometres of continent has tried to move westward in this central part of the boundary but has found nowhere to go — nowhere but up. Schellart says the same process is happening in mirror image on the other side of the Pacific, in the Japan subduction zone. But this collision has only been going on for less than 10 million years. "It's likely you'll get large mountain building there," he says. "It's in the initial stages." Other theories have been advanced for why the Andes are unusually high. Researchers have suggested it is because there are no rivers to wash sediments into the trench between this subducting plate and the continent, creating an unlubricated zone with extra friction to prop up the mountains. But Schellart points out that there are other subduction zones without sediment, such as the one off Tonga, that don't form big mountains. "It's a good global model," says Seth Stein of Northwestern University in Evanston, Illinois, who has worked on the Andes. "The insight that smaller boundaries can change shape more quickly is very nice," he says. This even helps to explain why the 'boot' of Italy has swung round so dramatically — it pointed directly north to south some 15 million years ago, but the evolving shape of the short subduction zone there has pushed the boundary around counter-clockwise. But Stein is doubtful that the model really answers all geologists' questions about the Andes. "The Andes are very much involved in the geology of the overriding continent, which isn't in their model," he says. - Schellart W. P., et al. Nature, 446 . 308 - 311 (2007). User Tools [+] Expand If you need help or have a question please use the links below to help resolve your problem.

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for National Geographic News Melting Greenland ice could cause oceans to rise by more than a foot (30 centimeters) over the next hundred years. The resulting sea level rise, spurred by global warming, may also happen three times faster than previously predicted. When all other sources of melting ice are also factored in—such as the Antarctic ice sheet and smaller glaciers—the sea level has been predicted to increase by several more feet by 2100, according to previous studies. (See a global warming interactive.) The new estimates are based on disappearance rates of the ancient Laurentide ice sheet that long ago covered North America and melted between 9,000 and 6,000 years ago. "We have never seen an ice sheet retreat significantly or even disappear before, yet this may happen for the Greenland ice sheet in the coming centuries to millennia," lead study author Anders Carlson, of the University of Wisconsin, said in a press release. Carlson said his team's research on the Laurentide ice sheet "gives us a window into how fast these large blocks of ice can melt and raise sea level." The study appears this week in the journal Nature Geoscience. At its peak, the Laurentide ice sheet was more than 5,000,000 square miles (13,000,000 square kilometers) across, with a thickness of up to 10,000 feet (3,000 meters) in some places, according to previous estimates. To determine the demise of the massive sheet, Carlson and his team estimated the ages of boulders left in its wake based on how long they had been exposed to cosmic rays. The geologists also obtained radiocarbon dates of trees and other organic materials that couldn't have existed until after the ice was gone. SOURCES AND RELATED WEB SITES

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With increasing height, air temperature within the troposphere and mesosphere drops uniformly with altitude at a rate of approximately 6.5 degrees Celsius per 1000 meters - known as the environmental lapse rate. However, sometimes this normal overall decline is reversed. A point or layer at which the temperature increases with height is called inversion or inversion layer. Temperature inversions frequently occur in anticyclones, but are also common in depressions when air in the middle troposphere subsides. Inversions may occur at any height, but the large temperature inversions at the tropopause and mesopause are stable and permanent features of the Earth's atmosphere. In the troposphere, the weather-sphere, inversions cause an increase in stability and tend to limit the upward growth of cloud, preventing further upward convection. When particularly strong, with high potential temperatures that suppress small-scale convection in the layers beneath them, they are often termed capping inversion. The lowermost layer of air frequently becomes an inversion layer known as surface inversion. The condition results, for example, from radiation cooling of the ground and the air above. This usually occurs when there is strong nocturnal radiation, after a clear, dry and starry night, called radiation night. Or from advection of warm air over cold surfaces. In wintertime, a temperature inversion occurs when cold air close to the ground is trapped by a layer of warmer air. As the inversion continues, air becomes stagnant and pollution becomes trapped close to the ground. Therefore inversions often cause the formation of smog. However, inversions and smog do also occur in summer and might turn into a serious respiration hazard over densely populated areas.

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Tip: Text Line Up How do I do it? Cut up a selection from a text or textbook into the number of students in class and pass out. Direct students to talk to one another and line up in the correct order of the text. When they think they are lined up correctly, students read their selection aloud. Make changes in position as needed and read again until the order makes sense. (Tip: Model how to do this with a simple example so students can see what is expected of them.) Variations & Extensions: Direct students to explain orally or write a few sentences describing the strategies they used to line up correctly. What did they learn about the structure of the text and text clues during this activity? Other line-ups include: lining up with key word cards in alphabetical order; lining up A-Z order by first or last name; lining up in chronological sequence for a scientific process or historical event; lining up to make a sentence with word and punctuation cards, lining up by birthdays, etc. Use picture cards instead of word or phrase cards for all or some students. Common Core ELA Speaking and Listening Standards 1&2 Prepare for and participate effectively in a range of conversations and collaborations with diverse partners, building on others' ideas and expressing their own clearly and persuasively. Integrate and evaluate information presented in diverse media and formats, including visually, quantitatively, and orally. Common Core ELA Reading Standard 5 Analyze the structure of texts, including how specific sentences, paragraphs, and larger portions of the text (e.g., a section, chapter, scene, or stanza) relate to each other and the whole. Everyday ELL is now Every Language Learner.

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Dividing with Remainders Lesson 17 of 23 Objective: SWBAT divide whole numbers by 1-digit divisors using manipulatives. In today's lesson, the students learn to use manipulatives to divide numbers by 1-digit divisors. They must consider the multiplication problem that supports their answer. This aligns with 4.NBT.B6 because the students find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. To get started, I ask the students a question. "When might you need to divide something in the real world?" I give the students a few minutes to think about the question. I take a few student responses. "When you want to share something with your friends," one student answered. "That is correct. " I tell the students, "Today, we will use manipulatives to help divide with a 1-digit divisor. Our multiplication facts will help us." Whole Class Discussion I call the students to the carpet as we prepare for a whole class discussion. The power point is already up on the Smart board. I like for my students to be near so that I can have their full attention while I'm at the Smart board. I begin by going over important vocabulary for this lesson. The students will have to know these terms to understand the lesson. quotient - an answer to a division problem divisor - a number by which another number is being divided dividend - the amount you want to divide remainder - the part that is left after you divide Thomas has 15 marbles. He wants to put the same number of marbles in 4 different containers. How many marbles will be in each container? How many marbles will be left as a remainder? First, I ask the students to identify what operation will be used to solve this problem. "Division," I hear most of them yell out. Based upon past knowledge, the clue words "same number" lets us know to divide. Therefore, this is a division problem. The problem is 15 divided by 4. Also, the key word "left" let us know that we are going to subtract to find the remainder. We can use our unit blocks to make a model of the problem. We know that there will be 4 groups. We can take our 15 unit blocks and begin to separate them into 4 groups, 1 by 1. Remember, that when you finish separating the unit blocks, there should be the same number of blocks in each group. The leftover unit blocks will be your remainder. The quotient to this problem is 3 because there are 3 marbles in each group (4 x 3 = 12). There will be 3 marbles left (15 - 12 = 3). Therefore, the remainder is 3. Let's try another one. Problem 2: 37 divided by 8. We can use our unit blocks to make a model of the problem. We know that there will be 8 groups. We can take our 37 unit blocks and begin to separate them into 8 groups, 1 by 1. Remember, that when you finish separating the unit blocks, there should be the same number of blocks in each group. The leftover unit blocks will be your remainder. The quotient to this problem is 4 because there are 4 items in each group (4 x 8 = 32). There will be 5 marbles left (37 - 32 = 5). Therefore, the remainder is 5. Group or Partner Activity I give the students practice on this skill by letting them work together. I find that collaborative learning is vital to the success of students. Students learn from each other by justifying their answers and critiquing the reasoning of others. For this activity, I put the students in pairs. I give each group a group activity sheet. The students must work together to find the quotient to the division problems. They must use the unit blocks or an other type of manipulative (MP5) to separate the dividend into groups. They must identify the multiplication number sentence that helps them solve this problem. A multiplication chart is attached to assist the students. They must communicate precisely to others within their groups. They must use clear definitions and terminology as they precisely discuss this problem. The students are guided to the conceptual understanding through questioning by their classmates, as well as by me. The students communicate with each other and must agree upon the answer to the problem. Because the students must agree upon the answer, this will take discussion, critiquing, and justifying of answers by both students. The students discuss the problem and agree upon the answer to the problem. As the pairs discuss the problem, they must be precise in their communication within their groups using the appropriate math terminology for this skill. As I walk around, I am listening for the students to use "talk" that will lead to the answer. I am holding the students accountable for their own learning. As they work, I monitor and assess their progression of understanding through questioning. 1. What is the dividend in this problem? 2. What multiplication problem will help find the dividend? 3. What is the remainder? How did you find the remainder? As I walked around the classroom, I heard the students communicate with each other about the assignment. I hear the classroom chatter and constant discussion among the students. Before Common Core, I thought that a quiet class working out of the book was the ideal class. Now, I am amazed at some of the conversation going on in the classroom between the students. As I walk around, I hear students say things like 'there has to be the same number in each group," "we need to take one away because it's not enough to put one in each group." Any groups that finish the assignment early, can go to the computer to practice the skill at the following site until we are ready for the whole group sharing: http://www.funbrain.com/math/index.html To close the lesson, I have one or two students share their answers. This gives those students who still do not understand another opportunity to learn it. I like to use my document camera to show the students' work during this time. Some students do not understand what is being said, but understand clearly when the work is put up for them to see. I feel that by closing each of my lessons by having students share their work is very important to the success of the lesson. Students need to see good work samples, as well as work that may have incorrect information. More than one student may have had the same misconception. During the closing of the lesson, all misconceptions that were spotted during the group activity will be addressed whole class. The biggest misconception that I saw during this lesson was that some of the students used a multiplication problem that gave a product that was larger than the dividend. For example, with the division problem of 43 divided by 6, some students used the multiplication problem of 6 x 8 = 48. During the closure, we discussed that fact that you cannot use a number larger than the dividend. This is just our first week working with division. Some of the student progress has been very inspiring. We will continue to work on the skill.

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This color coded number chart is an effective visual tool to teach students the patterns of skip counting and number factors. Note that each factor 2-12 is a different color. The factors for each number are color coded in the dots above the number on the chart. Students can keep this number chart in their math folders as a handy tool. There are many ways to use the color coded number chart: Skip Counting – Start with two and count the red numbers. Start with three and count the yellow numbers, etc. Look at the pattern of the colors. Multiplication – For the problem 3 x 4, start with yellow and skip count four yellow dots. 3 – 6 – 9 – 12 3×4 =12 Prime numbers – Except for 3, 5 and 7, the prime numbers have zero colored circles, showing that it is only divisible by one and itself. This comes in handy when students are trying to reduce fractions. If the denominator is a prime number, it cannot be reduced. Least Common Multiple – To Find the LCM of 3 and 4 look on the chart to find the lowest number that has both a yellow and green circle. LCM of 3 and 4 is 12. Greatest Common Factor – To Find the GCF of 21 and 28 look above the numbers 21 and 28 to see what colors they both have. Check the color chart to find the largest common factor of the two numbers. GCF of 21 and 28 is 7 (purple) Click here to download the color coded number chart. There is also a blank chart, so the students can color in the factors as they learn them. Have some white-out handy, as they might make some errors. 🙂

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Tundra — also called barren land — is a large region of the Northern Hemisphere lacking trees and possessing abundant rock outcrops. Tundra — also called barren land — is a large region of the Northern Hemisphere lacking trees and possessing abundant rock outcrops. In Canada, the southern boundary extends from the Mackenzie Delta to southern Hudson Bay and northeast to Labrador. Many climate variables combine to determine the position of this boundary. The tundra environment is characterized by the general presence of permafrost (except beneath some lakes and rivers); short summers with almost continuous daylight; long winters and “arctic nights"; low annual precipitation (hence the name “polar desert”); strong winds and winter blizzards; discontinuous vegetation; unstable, wet soil conditions resulting from permafrost and frost action. The term "alpine tundra" has been used for areas above the treeline in mountain areas. Although alpine tundra resembles Arctic tundra in some respects, the differences are significant. (See also Physiographic Regions.) Flora and Fauna Tundra plants tend to be perennial and have short reproductive cycles. Their seeds are effectively dispersed by wind, and some species are capable of vegetative propagation (i.e. asexual reproduction). Plants in the region include lichens, mosses, grasses and low shrubs. Tundra plants have developed many adaptations for survival. Their low stature exploits the more favourable microclimate near the ground, while small, leathery, hairy leaves prevent moisture loss by evaporation. Many birds and some animals live in the tundra in summer, migrating in autumn (see Arctic Animals). Tundra environments present many impediments to human activities. Buildings, pipelines, roads and airports must be constructed so that they can cope with cold climate and permafrost, and proper advance planning must precede resource development and waste disposal to avoid damage to ecosystems.

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The Music Explorer is a teaching tool that can be used in many different ways to support musical learning. Below are 10 ideas to help you get started. Perhaps choose a style of music which links with a piece you will be playing during the lesson. First find the pulse using body percussion and then with voices or instruments. Use the track as a backing for a copy back activity using one or more pitches. This can be teacher led initially but then allow the pupils to take the lead and improvise their own phrases in pairs or groups. Develop the idea to a question and answer activity, starting with short phrases. Again, encourage the students to take the lead but always make sure they are able to repeat their own improvised question. This will focus their attention! Choose a style that will appeal to your students eg Bollywood and discuss why it sounds like Bollywood. What are the musical clues? Using just one note, or more if you prefer, can you/the children sing or play short patterns in the same style? Discuss. There are varying tempo options for the styles. What impact does the speed have on the style? Together with the students compose a simple phrase/piece. Sing or play this piece using different style backings. How does the backing affect the phrase/piece? Do they have a favourite style for this particular example? Why? Take a short rhythmic or melodic phrase/riff from a piece you are singing or playing and use this as a starting point for composing a short piece using the explorer tool. Try repeating the idea at the same or a different pitch, reversing it, stretching it, making up an answering phrase and so on. Using the most appropriate form of notation for your students compose four simple two bar rhythmic or melodic phrases/riffs, then play back one of them. Can they tell you which phrase it was? Ask them to sing or play the phrase/riff of their choice, which one did they perform? This can be challenging for both the players and the listeners. Sing or play a simple rhythmic phrase and ask your pupils to write this down using blocks or notation. Extend the complexity of the rhythm or melody as they progress. Explore simple notation rules by adding too many or too few beats into a bar eg adding a minim and a dotted minim into the same bar. What happens? Once they have successfully created a correct example sing or play it through together.

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Current is measured in Amps (A) using an Ammeter Voltage is measured in Volts (V) using a Voltmeter Voltage = Current x Resistance The resistance in a circuit can be increased by adding more components, such as resistors and lamps. The diagram below shows the standard circuit symbols you need to know. Two things are important for a circuit to work: - there must be a complete circuit - there must be no short circuits A current flows when an electric charge moves around a circuit. No current can flow if the circuit is broken, for example, when a switch is open…

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Learn all about adding two-digit numbers and adding three-digit numbers in this free lesson, which includes practice problems. On the last page, you practiced adding vertically stacked numbers. Some problems need an extra step. For example, let's look at the following problem: Our first step is to add the digits on the right— 5 and 9. However, you might notice there isn't room to write the sum, 14. When the sum of two digits in a math problem is greater than 9, the normal way of adding stacked numbers won't work. You'll have to use a technique called carrying. Let's see how it works. We'll try this problem, 25 + 39. As usual, we'll start by adding the digits on the right. Here, that's 5 and 9. 5 + 9 is 14, but there's no room to write both digits in 14 underneath the 5 and 9. We'll write the right digit, 4, under the line... We'll write the right digit, 4, under the line... then we'll carry the left digit, 1, up to the next set of digits in the problem. Do you see what we did? Our sum was 14. We put the 4 underneath the line, and carried the 1 and placed it above the next set of digits. Next, we'll add the left digits. Since we carried the 1, we'll add it too. 1 + 2 + 3 is 6, so we'll write 6 below the line. We're done. 25 + 39 = 64. Let's practice with one more problem: 178 + 42. As always, start by adding the digits on the right. Here, that's 8 + 2. 8 + 2 is 10, so it looks like we'll have to carry. The 0 stays underneath the 8 and the 2. Carry the 1 and place it above the next set of digits to the left. Now move left to add the next set of digits. Since we carried the 1, add it too. 1 + 7 + 4 = 12. Put the right number, 2, under the digits we added. Carry the 1 and place it above the next column to the left. To finish, add this column. Remember to include the 1 we just carried. 1 + 1 + nothing is 2, so we'll write 2 underneath the 1. We're done. Our answer is 220. 178 + 42 = 220. As you carry, be careful to keep track of the various numbers. If you're writing problems down, be sure to write the carried digits in small print above the column of digits to the left. Solve these problems by carrying. Then, check your answer by typing it in the box.

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About This Chapter Algebraic Expressions and Equations - Chapter Summary These lessons break down the steps for evaluating, combining, simplifying, writing and solving algebraic problems. Prepare for test questions related to these areas through our online video lessons. Some of the topics and skills covered in this section include: - Writing arithmetic expressions - Evaluating math formulas - Writing and simplifying algebraic expressions - Combining like terms - Writing equations with inequalities - Linear, quadratic and polynomial equations - Solving one-step and multi-step problems - Problem solving with the addition and multiplication principles - Equations with parentheses - Problems with infinite or no solutions - Translating equations to word problems This chapter includes short video lessons taught by experienced instructors. The lessons use fun illustrations and real-world examples to present their points. Additional resources include transcripts that highlight vocabulary terms, self-assessment quizzes and a chapter exam. TASC Math Objectives The TASC test is an alternative to earning your high school diploma. It assesses your knowledge in five subject areas, one of which is math. The mathematical reasoning portion of this test measures your skills in five content areas: algebra, statistics, numbers and quantity, functions and geometry. Algebra questions make up 26% of the test and test your ability to: - Apply algebraic rules to solve equations - Compute algebraic expressions - Isolate quantities of interest Multiple-choice, gridded-response, constructed-response and technology-enhanced formatted questions all appear on the test. Our lessons give you the help you need with the steps and operations needed to solve these problems. 1. What is the Correct Setup to Solve Math Problems?: Writing Arithmetic Expressions When it comes to solving math word problems, there is a correct way of setting up the problem and labeling the various parts of the problem so that you can solve the problem easily. Watch this video lesson to learn how you can do it. 2. Understanding and Evaluating Math Formulas With all the formulas out there, how do you know which one to pick? And how do you read formulas anyways? Watch this video lesson and you will find the answers to these questions. 3. Expressing Relationships as Algebraic Expressions What do you do when you don't know what a number is but you do know how it relates to something else? You use an algebraic expression. In this lesson, we'll learn how to express relationships as algebraic expressions. 4. Evaluating Simple Algebraic Expressions In this lesson, we'll learn how to evaluate algebraic expressions, which involves substituting numbers for variables and following the order of operations. By the end of the lesson, you'll be an algebraic expression expert. 5. Combining Like Terms in Algebraic Expressions When you have an algebraic expression that's much too long, it would be great if you could simplify it. That's when knowing how to combine like terms comes in. In this lesson, we'll learn the process of combining like terms and practice simplifying expressions. 6. Practice Simplifying Algebraic Expressions In this lesson, we'll practice simplifying a variety of algebraic expressions. We'll use two key concepts, combining like terms and the distributive property, to help us simplify. 7. Negative Signs and Simplifying Algebraic Expressions Don't let negative signs get you down. In this lesson, we'll stay positive as we practice simplifying algebraic expressions that have those tricky negative signs. 8. Writing Equations with Inequalities: Open Sentences and True/False Statements After watching this video lesson you will be able to write open sentences and true or false statements that use inequalities. You will also be able to solve and/or determine whether a particular inequality is true or false. 9. Common Algebraic Equations: Linear, Quadratic, Polynomial, and More Watch this video lesson to see the kinds of equations that you will come across most often in algebra. Learn to distinguish them by just looking for the identifying components of each equation. 10. Defining, Translating, & Solving One-Step Equations Watch this video lesson to learn how you can write a simple math equation when you are given a word problem. Learn how to translate words into math symbols. Learn the shortcuts to remember. 11. Solving Equations Using the Addition Principle In algebra, we have certain principles that we use to help us solve equations quickly and easily. The addition principle is one of them. Watch this video lesson to learn how you can apply it to solve your equations. 12. Solving Equations Using the Multiplication Principle When it comes to solving equations in algebra, one of the essential skills you need is the ability to multiply. Watch this video lesson to learn how you can use the multiplication principle to isolate your variable. 13. Solving Equations Using Both Addition and Multiplication Principles Most times in algebra, to solve for your variable, you will need to perform more than one operation to get your answer. Watch this video lesson to learn the proper steps to take to solve these equations. 14. Collecting Like Terms On One Side of an Equation When you are using algebra to solve your problems, one of your biggest and most often used methods is that of collecting like terms. Watch this video lesson to see how it is done. 15. Solving Equations Containing Parentheses When we have parentheses in our equations it changes the way we solve them. Now we have an added step to do to remove those parentheses. Watch this video lesson to learn how it is done. 16. Solving Equations with Infinite Solutions or No Solutions In algebra, there are two scenarios that give us interesting results. Watch this video lesson to learn how you can distinguish problems that have no answers and problems that have an infinite number of answers. 17. Translating Words to Algebraic Expressions When it comes to word problems, the easiest way to solve them is to look for keywords and change them into math symbols. Watch this video lesson to find out what keywords you should look for and what math symbols they represent. 18. How to Solve One-Step Algebra Equations in Word Problems Word problems may be considered the most evil math invention ever, but never fear! Just watch this video lesson and you will know how to methodically translate these word problems into simple math and then to solve it. 19. How to Solve Equations with Multiple Steps In algebra, when you want to solve an equation for a particular variable, you will need to perform multiple steps that include adding, subtracting, multiplying, and dividing. Watch this video lesson to learn the order you need to do these steps. 20. How to Solve Multi-Step Algebra Equations in Word Problems After watching this video lesson, you will be able to solve word problems like a pro. Learn how to setup your problem, write your equations and then solve your equations to find your answer. Earning College Credit Did you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level. To learn more, visit our Earning Credit Page Transferring credit to the school of your choice Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you. Other chapters within the TASC Mathematics: Prep and Practice course - TASC Math: Real Numbers - TASC Math: Complex and Imaginary Numbers Review - TASC Math: Exponents and Exponential Expressions - TASC Math: Radical Expressions - TASC Math: Functions - TASC Math: Graphing and Functions - TASC Math: Inequalities - TASC Math: Algebraic Distribution - TASC Math: Linear Equations - TASC Math: Factoring - TASC Math: Quadratic Equations - TASC Math: Graphing and Factoring Quadratic Equations - TASC Math: Properties of Polynomial Functions - TASC Math: Rational Expressions - TASC Math: Measurement - TASC Math: Geometry - TASC Math: Calculations, Ratios, Percent & Proportions - TASC Math: Data, Statistics, and Probability - TASC Math: Trigonometry

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From Guess and Check to Creating Equations; From Equations to Inequalities Lesson 2 of 8 Objective: SWBAT practice using the guess-and-check strategy as a method for developing equations. The purpose of today's opener is to help students see the relationship between solving linear equations and solving linear inequalities. I give students a few minutes to get started, and I circulate to see how they're doing. Nearly all students can solve #1, a two-step equation, and most are confident with solving #3 as well. Some have already come to understand that there's little difference between solving equations and inequalities, and before we get to discussing the one difference between the two, I want to dispel some of the anxiety that surrounds those inequality signs by showing kids that this really is the same thing. I don't go over the steps for solving the first equation. I just ask what everyone got, and record the answer, x = 6, on the board. I say, "Now, what this solution means is that if we replace the x with a six in this equation, then the equation will be true. That's what it means to solve an equation." Next, beside second question, I write x < 6, and say, "The steps to solve the inequality in number two are exactly the same. It's just that the solution will look like this." I point to my solution, pause, and continue, "How many numbers are equal to six?" We all agree that only six is equal to six. So in an equation there's just one solution. "But how many numbers are less than six?" Someone is always quick to shout "Six!" and then we recall that all of the negative numbers would work as well. So there are a lot of number that are less than six. You might even say an infinite amount. "The key here is that any number less than six will make this inequality true," I say, before asking for such a number. We take suggestions and substitute them in for x, noting that each makes the inequality true. This whole exchange takes maybe a minute. Then we take a look at problems #3 and #4. There are two reasonable methods for solving the equation in #3, and I don't prioritize one over the other. Instead, I elicit suggestions from students, and it usually doesn't take too much effort to end up with the two solution strategies you see here. Of course, the right-hand example has the flaw of employing common sense instead of algebraic manipulation in the final step, which offers another great opportunity to start a conversation. It's neat to hear students express preferences for one or the other, and I think that this activity helps to open up the idea of algebra as a flexible language that can be molded in different ways. When we move to the inequality version of the problem in #4, however, simply "bringing down" the less than sign yields two different results. The question I pose to the class is, "Which one is right?" If they have trouble following me, I try to get them to acknowledge that it can't be both, and it must be one. "There are numbers that are greater than 7 and numbers that are less than 7, but no numbers are both greater than and less than 7, right?" This is where we check our work. I have students choose one of each sort of number, and substitute them into the original equation. We see which one works. If a class is getting this quickly here, I'll dig into the solution step of "turning around" the inequality sign when we multiply or divide by a negative number. In other classes that are just hanging on, the takeaway is that it's always worth it to check an answer to an inequality. Either way, I tell students to keep this in mind as we continue to work with inequalities. We spend a short amount of time today digging back into the group problem solving that began in yesterday's class. My goal is for every class to advance by gaining one tidbit of knowledge today. Precisely what that one tidbit is depends on how the class did yesterday. I cover my introduction to this group problem solving in yesterday's lesson; if you haven't already, please take a look at that lesson for an overview of the work that continues here. That lesson goes differently every time, so there are variety of points from which we may be starting today. There may still be some algebraic generalization to do with Vanessa's Raise, we may be ready for a clean start on Ed's Book, or if things went very quickly yesterday, students may already be started on that second problem. Whatever the case, the purpose of these two problems is to establish a structured form of guess and check, and then to use that form to develop equations that can be used to solve those problems. In the "Ed's Book" problem, we can once again apply the "before and after" structure: there was the amount of the book that Ed had read before reading those 84 pages, and amount that he'd read after. If they need help, I'll help students set that up. Setting up guess and check is one possible takeaway for today's lesson. For other kids an analysis of wrong guesses is what gets them going. It would be impossible to overemphasize the way that introducing such a line of thinking can draw students in. A structure like this serves struggling students by showing them how to be self-sufficient, and it furthers the thinking of advanced students by framing another linear relationship (ie. if my guess increases by this much, then the result changes like this.) Some kids think we shouldn't guess and check if the goal is to create equations. I explain that guess and check is precisely what helps us to create those equations! What we're working toward is the ability to take the unknown - the number that we keep guessing at - and replace it with a variable. We can then take that variable and place it in an equation. Again, the precise pace of how this knowledge rolls out to students depends on the class. Some students were ready to dig into this idea yesterday, for others it might be the thing to examine right now, and for others, that will be the focus of tomorrow's lesson. Mastery Quiz: SLT 1.1 The latter half of today's class is spent on a Mastery Quiz for SLT 1.1. I want to see how well students can solve equations and inequalities, and show their steps, in a short amount of time. For those who have achieved mastery, this is a chance to show it. For those who are still working toward it, this is a chance to build a little urgency and facility with these skills, under the pressure of clock. Here is the quiz: Mastery Quiz SLT 1.1. I project it on the screen. On the first page are the two learning targets I'll assess here: 1.1 and MP1. After instructing students to take out a sheet of paper and write a perfect heading, I say that I'm looking for and assessing two things with this quiz. I want to see if they can solve each equation and inequality correctly, and therefore demonstrate their level of mastery on SLT 1.1. I also want to see that they can clearly show their work, which demonstrates that they're persevering and making sense of each problem. I ask if everyone is ready, then I put the first equation on the screen. This quiz moves from a Level 1 equation to a Level 7 equation over the course of 15 problems, I put them up one or two at a time, each with time limits. The allotted time for #'s 1-14 adds up to 18 minutes; to allow time for #15 and instructions, you'll want a little more time than that. If anyone finishes solving an equation early, I say that they can record some of the properties that justify their solution in the margin. It's always interesting to see how different students respond to a race against time. For some, this is finally the thing that gets them to focus all of their energy on their work. For others, it's quite stressful, and when we debrief this quiz tomorrow, I'll want to help those students think about how panic probably doesn't help, and what we can do instead. In any case, this is a strategy to be used sparingly. During the quiz, there are always some students who say they love it, and some will say they hate it. In terms of skill development and test-anxiety-management, this structure yields positive results.

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In this section we are going to submerge a vertical plate in water and we want to know the force that is exerted on the plate due to the pressure of the water. This force is often called the hydrostatic force. There are two basic formulas that we’ll be using here. First, if we are d meters below the surface then the hydrostatic pressure is given where, ρ is the density of the fluid and g is the gravitational acceleration. We are going to assume that the fluid in question is water and since we are going to be using the metric system these quantities become, The second formula that we need is the following. Assume that a constant pressure P is acting on a surface with area A. Then the hydrostatic force that acts on the area is, Note that we won’t be able to find the hydrostatic force on a vertical plate using this formula since the pressure will vary with depth and hence will not be constant as required by this formula. We will however need this for our work. The best way to see how these problems work is to do an example or two. Example 1 Determine the hydrostatic force on the following triangular plate that is submerged in water as shown. The first thing to do here is set up an axis system. So, let’s redo the sketch above with the following axis system added in. So, we are going to orient the x-axis so that positive x is downward, corresponds to the water surface and corresponds to the depth of the tip of the Next we break up the triangle into n horizontal strips each of equal width and in each interval choose any point . In order to make the computations easier we are going to make two assumptions about these strips. First, we will ignore the fact that the ends are actually going to be slanted and assume the strips are rectangular. If is sufficiently small this will not affect our computations much. Second, we will assume that is small enough that the hydrostatic pressure on each strip is essentially constant. Below is a representative strip. The height of this strip is and the width is 2a. We can use similar triangles to determine a as Now, since we are assuming the pressure on this strip is constant, the pressure is given by, and the hydrostatic force on each strip is, The approximate hydrostatic force on the plate is then the sum of the forces on all the strips or, Taking the limit will get the exact hydrostatic force, Using the definition of the definite integral this is nothing more than, The hydrostatic force is then, Let’s take a look at another example. Example 2 Find the hydrostatic force on a circular plate of radius 2 that is submerged 6 meters in the water. First, we’re going to assume that the top of the circular plate is 6 meters under the water. Next, we will set up the axis system so that the origin of the axis system is at the center of the plate. Setting the axis system up in this way will greatly simplify our work. Finally, we will again split up the plate into n horizontal strips each of width and we’ll choose a point from each strip. We’ll also assume that the strips are rectangular again to help with the computations. Here is a sketch of the setup. The depth below the water surface of each strip is, and that in turn gives us the pressure on the strip, The area of each strip is, The hydrostatic force on each strip is, The total force on the plate is, To do this integral we’ll need to split it up into two The first integral requires the trig substitution and the second integral needs the substitution . After using these substitution we get, Note that after the substitution we know the second integral will be zero because the upper and lower limit is the same.

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In this Section: In this section, we start digging into the basics of algebra and introduce the equation. We learn how to tell the difference between an equation and an algebraic expression. When we have an equation, we have two algebraic expressions that are separated by an equals sign. This equation can be solved and the answer can be checked. When we have an algebraic expression, there is no equality symbol. We only gain a value for the algebraic expression if a value for the variable is given. In this case only, we can substitute in for the variable and obtain a value for the algebraic expression. We then move on and learn how to determine if a given value is a solution to an equation. We do this by replacing the variable in the equation with our proposed solution. If after simplifying, the left and the right side are equal, meaning the same value, then our proposed solution is an actual solution.

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On this day in history, July 1, 1776, a Cherokee war campaign against the southern colonies begins. The Cherokee tribe was traditionally located in the area of northern Georgia, western North Carolina and eastern Tennessee. Warfare arose periodically between the Cherokee and the encroaching white settlers from the time of their first contact, but a new wave of conflict arose after the French and Indian War. The Proclamation Line of 1763 forbade British settlers from settling west of the Appalachians in an effort to limit conflict between settlers and Indians who had supported the British against the French during the war. Some settlers had other ideas though and tried to settle in the area. In the late 1760s and early 1770s, the first several settlements began in what is now eastern Tennessee in Cherokee territory. The settlers believed they were in western Virginia, but a survey proved they were actually outside colonial territory. They were ordered to leave the Cherokee territory by the British Superintendent of Indian Affairs. The Cherokee chiefs, however, said they could stay as long as no more settlers came. Click to enlarge Shows the Cherokee settlements (light brown) involved in the July, 1776 campaign In 1775, Richard Henderson of North Carolina made a deal with Cherokee leaders to purchase most of modern day Kentucky. The sale did not take into account the fact that other tribes claimed this land, nor the fact that it was illegal according to British law as defined by the Proclamation Line of 1763. The "sale" caused a rift in the Cherokee tribe. A young rebel named Dragging Canoe angrily challenged the older leaders who made the deal and started gathering a coalition around him of those who were disenchanted with their elders for making deals with and selling land to the settlers. When the American Revolution broke out, the settlers in Cherokee territory decided that British law no longer applied to them and they could live wherever they wanted. Since they had made a treaty with the Cherokee, they were on the land legitimately in their view. In May of 1776, a coalition of northern tribes allied with the British convinced Dragging Canoe and his band to join them in fighting the colonists. A plan was hatched whereby simultaneous raids would be led against the settlers in Cherokee territory, as well as on frontier settlements in Virginia, North and South Carolina and Georgia. The campaign began on July 1, 1776. In some places, settlers had been warned and took refuge in various forts. In other places, settlers were massacred and homes and villages were destroyed. The Cherokee attack led to a massive response from the combined colonial militias of the attacked colonies. Thousands of militia members marched on Cherokee territory, burned dozens of villages, destroyed crops and killed those who resisted. Even those who were not involved in the attacks suffered. Over a period of several months, the Cherokee campaign was put down with a resounding colonial victory. The colonial victory led to peace treaties established with the older and wiser Cherokee chiefs who understood they could not win this fight. The younger Dragging Canoe moved south with a growing group of rebels where he continued to work with the British and launch attacks against white settlers for years to come, which were known as the Chickamauga Wars, named for the region in which Dragging Canoe settled near modern day Chattanooga, Tennessee.

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What Does a System of Equations Really Look Like? Lesson 2 of 13 Objective: The objective of this lesson is to create a link between the algebraic representation of a situation and the graphical representation. This lesson will focus on the appearance of systems of equations in two variables. Students will build meaning by determining the solution to a system by an inspection of the coordinates that make up each equations graph. Without a graph, students will determine some coordinates that would lie on two lines by using the equations. Students should be encouraged to determine points by looking at the structure (MP7) of the equation (for example x + y = 3, what two numbers add up to 3?) Students are asked to list seven points to encourage them to see the pattern extending into the negative values as well as the positive values. Then, by inspection students can determine the solution point (if possible from their values) and verify their findings by graphing the two equations. Students will also look at the three cases for a system of linear equations, namely, no solutions, one solution, and infinite solutions. Again, this can be done both by looking at the structure of the equations (parallel lines, lines that intersect, or the same line) and then students can use a graphing calculator to see how the graphs of each of these cases appears. Lastly, students will be modeling a situation algebraically that involves two constraint equations set in a real world context. As a ticket out the door, students will have a choice of two assessments of learning. Both will give you valuable information about how to structure groups of students for the next days lesson. The target level question requires students to see how the stucture of the system leads to no solution (parallel lines). The more complex question assesses students understanding that lines extend infinitely in both directions and that if two lines do not have the same slope they will eventually intersect.

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This is covered by: AQA 8035, Cambridge IGCSE, CEA, Edexcel A, Edexcel B, Eduqas A, OCR A, OCR B, WJEC Longshore drift is the name given to the process by which beach material is transported along the coast by the action of waves. Waves rarely hit the beach at exactly right angles to the coast, and are far more likely to hit the beach at an angle. This is because in many areas the prevailing wind controls the direction of the waves and, obviously, very few long sections of coast are dead straight for miles and miles. As waves approach a beach the base of the wave hits the sea bed. This is what causes it to topple forward and to ‘break’ but it also allows the wave to pick up sediment. The size of the sediment particles moved by the wave is determined by what is available on the sea bed, and by the power of the wave. More powerful waves can move heavier sediment particles. If the wave was to hit the beach at exactly right angles to the line of the coast, the water would go straight up the beach (swash) and straight back down again (backwash). The only movement of the sediment would be up the beach with the swash, and back down the beach with the backwash. When waves break on to a beach at an angle, material is pushed up the beach at the same angle by the swash, but pulled back down the beach by the backwash at ninety degrees to the coast. The sediment is moved across the beach as well as up it. When the wave runs out of energy the water starts to flow back towards the sea. Gravity pulls it straight down the beach, so the returning water follows a different path to the one it followed on the way up it. Each wave can move the sediment a little further across the beach. The photograph shows a series of wooden groynes stretching down a sand and shingle beach. You can see that this side of the nearest groyne, protected from the waves, has become an area of deposition where sediment is built up. On the other side of the groyne the beach level is lower because it is an erosional environment where sediment cannot settle. On many beaches you can find height differences of several meters on different sides of a groyne. Many a beach walker has had a nasty surprise when leaping over a low groyne and finding a drop the other side! A riprap armoured groyne interferes with longshore drift at Hengistbury Head. Longshore drift comes from the right of the image, transporting beach sediment along the coast from right to left. You can see that on the right-hand side of the image the beach is quite narrow and the waves have enough energy to form white tops. This is an area being eroded by the longshore drift; more material is removed than is deposited. On the sheltered left-hand side of the photograph the waves have less energy (no breaking white waves) and the beach is much wider due to the groyne protecting the area and leading to increased deposition. Deposition always occurs on the side of a groyne protected from longshore drift, whilst erosion occurs on the side exposed to it. This photograph was taken when standing on a groyne and looking up the beach. A wave has just broken and you can see that the water has travelled considerably further up the beach on the right-hand side of the groyne compared to the left-hand side. This is because there is less sediment on the beach on the right-hand side than on the left. From this observation you can determine that erosion is strongest to the right of the groyne and deposition is predominant to the left of it. The conclusion is that longshore drift is operating from the right of the image, pushing sediment towards the left.

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number of factors, ocean currents and water movements play a big role. Some currents take warm water away from the equator, influencing coastal climates near the poles. Others take colder water from the poles or the deep ocean and move it towards the equator, creating cooler coastal climates. The main driver of ocean surface currents is wind. However, the earth’s rotation and continental positioning also play a big role. Deep sea currents are mainly induced by density differences between the surface water and the deep water. A lot of continents or large landmasses have coastal currents which transport nutrients and heat, while the deep oceans have various currents which differ depending on their location and the surrounding geography¹. Oceanic currents influence the climate due to their ability to transport heat. The ocean itself acts as a vital climate buffer, as it absorbs the majority of the excess atmospheric heat which is trapped by climate change. Some figures suggest that around 90% of the excess heat trapped through global warming is absorbed by the ocean, with negligible temperature changes². North or South moving currents have the ability to transport water huge distances. This water can then cool or warm the surrounding air, which indirectly influences the temperature of the nearby land. For example, the climate of coastal areas of Western Europe are a lot milder than would be expected for this altitude. This is due to the ‘Gulf Stream’, which carries warm water from the Atlantic Ocean in a northerly direction¹. Due to various factors, including evaporation and surface cooling, surface water can often become denser than the deeper water. This can create vertical, circular currents which are often referred to as “convective currents” or “convective turning”³. Often, this type of current acts in a way that it takes warm water from the equator, moves it poleward, where it cools and sinks, completing the circular current. This disperses heat from near the equator towards the poles, making some areas a lot warmer than they would otherwise be. Without circular currents like these, may of the northern and southern extremities of human habitation would be rendered too cold to live in. Additionally, without this method of heat dispersal, areas near the equator would become a lot hotter, and perhaps even become inhabitable. This would drastically change the world as we know it¹. An example of the huge impact even a small change in currents could have In a study by Manabe and Stouffer (1993), the impact of increasing atmospheric carbon dioxide concentrations was analysed. They found that with significant CO2 concentration increases, the impact of the Atlantic convective currents was significantly decreased. With a four-fold increase in CO2, it was predicted that the current would begin to slow, and eventually stop over a period of 100 to 200 years. This would cause the climate of much of Western Europe to change, and would impact billions of people world-wide. This little known fact about global warming gives just one more example of its hidden effects and the associated unexplored issues⁴.

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An object's momentum is the product of its velocity and mass. The quantity describes, for instance, the impact that a moving vehicle has on an object that it hits or the penetrative power of a speeding bullet. When the object travels at a constant speed, it neither gains nor loses momentum. When two objects collide, they again together gain and lose no momentum. The only way for a body to gain momentum is for an external force to act on it. Divide the magnitude of the external force on the object by the object's mass. For this example, imagine a force of 1,000 Newtons acting on a mass of 20 kg: 1,000 ÷ 20 = 50. This is the object's acceleration, measured in meters per second squared. Multiply the acceleration by the time for which the force acts. If the force acts, for instance, for 5 seconds: 50 --- 5 = 250. This is the object's change in velocity, measured in m/s. Multiply the object's change in velocity by its mass: 250 --- 20 = 5,000. This is the object's change in momentum, measured in kg m/s. - Photo Credit Photodisc/Photodisc/Getty Images

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Parsing sentences involves identifying the function of each word. Formal English grammar used to be taught in school regularly in the belief that this would improve students' correct usage of the language. However, research showed that completion of formal grammar exercises had a minimal positive effect on students' written compositions. Parsing sentences fell out of favor. Today educators say class time is better spent engaging in writing in context. Nevertheless, it is useful for students to be able to identify the parts of speech and understand their function in sentences. Knowing how to parse a sentence may be beneficial to students learning English as a second language. Select a short sentence from a newspaper, magazine or book. Copy the sentence into your notebook. Leave a blank line in between each line of writing. Read the sentence aloud. Visualize the meaning of the sentence. Decide what is the main action of the sentence. For example, in the sentence, "The young man who stole the money ran quickly down the street," the main action is the running, so the word "ran" is the main predicate of the sentence. Examine the sentence to determine whether there are words that are add further description to the main predicate. In this example the descriptors are "quickly down the street." Try asking yourself the questions, "how?" "where?" and "why?" about the main predicate, in this example, "ran" to help you find the descriptors. Draw a double line under all the words in the complete predicate. In this example, "ran quickly down the street." Note that this predicate tells you the action -- "ran" as well as where and how the running occurred. Draw a line with a different colored pencil under the word "ran" to identify it as the main predicate. Identify the doer of the action of the main predicate. Ask yourself the question "who did the action?" In this example, you will ask, "who did the running?" or "who ran?" Draw a single line under the doer of the action or the subject. In this example, the main subject is "man". Examine the sentence to determine whether there are words that are add further description to the main subject. In this example the descriptors are "the young man who stole the money." Try asking yourself the questions, "what kind of?" or "which?" about the main subject, in this example, "man" to help you find the descriptors. Draw another line under the complete subject using a different colored pen. In this example the complete subject is, "The young man who stole the money." Repeat steps 1 through 8 for additional sentences to give yourself more practice. Keep in mind that parsing sentences consists of identifying the main subject and complete subject as well as the main predicate and complete predicate of a sentence. In addition, parsing includes identifying the words which modify or describe the subject and predicate. Develop a color-coded system of symbols to help you distinguish the modifying words as you parse the sentences. Use different colors or marks such as round or square brackets to identify adjectives such as "young" and clauses such as "who stole the money." Things You Will Need - Knowledge of parts of speech - Text material - Colored pens or pencils - Purchase a grammar text or examine online resources. Study further details regarding grammatical components of sentences such as clauses as well as information about the parts of speech. - Start with shorter sentences until you have mastered the skill of parsing sentences. Longer sentences with multiple clauses will only confuse you when you are beginning to understand these grammatical rules. - ATEG: The Assembly for the Teaching of English Grammar - College English; "Grammar, Grammars, and the Teaching of Grammar; "Patrick Hartwell; February 1985 - Encyclopedia.com: Parsing - Comstock/Stockbyte/Getty Images

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Learning to code may not be for everyone, but as technology continues to reach deeper into our lives, an ability to understand and participate in it has become increasingly important. But more than that, programmatic thinking offers tools for strategizing, problem-solving and creativity that can be useful in everyday life. This is why DUAL was created. Many computer programs are built with three common patterns: selection, sequence and loop. Playing DUAL introduces all of these concepts. When you use conditions you're testing to see if shapes on the grid return TRUE or FALSE. If a shape matches the condition, it will return TRUE. If it doesn't match, it returns FALSE. In code these are called conditional statements. You can see how these work in the game below. During each step of the sequence, the program loops through the shapes on the grid and checks which return TRUE. Shapes that pass these 'tests' are grouped and targeted by whichever action the player chose. Shapes that return false are faded out. See below for more about sequences and loops. When you use the AND / OR logic in the game, you're using logical operators. With AND between two conditions, the program returns TRUE if both conditions are met. With OR the program returns TRUE if either condition is met. Consider what this would mean if you combined two of the above conditional statements. A program reads code in sequential order, responding to changing states as it goes along. This is exactly how sequences work in the game! The program reads the code from top to bottom. After the first condition is tested and the first action is taken, the program moves to the next step. At this point the next condition is tested, but the shapes on the grid have now changed. Being able to anticipate such changes and plan ahead is key to playing the game – and key to being good at programming. When you hit play, the program loops through every shape on the grid: first to check if each shape meets your set of conditions and then to perform each action in your sequence. Let's see what the loop returns for the conditions below. Loops are used all the time in programming to go systematically through a set of items or objects. Sometimes this is to find things, or test conditions like above. Sometimes it's to collect or change things. Computers are great at repetitive tasks that people would find boring. DUAL wasn't designed to teach players how to code, but to get them started thinking programmatically. Many programmers would agree that writing code isn't actually the hard part – figuring out the logic for a program is. If the concepts in DUAL make sense to you then you've already taken a huge leap! Thinking programmatically is really about thinking in terms of systems. The world is full of systems – making programmatic thinking an invaluable skill. The web is brimming with great resources for learning programming. Here are some next steps:

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A current can be induced in a conducting loop if it is exposed to a changing magnetic field. This change may be produced in several ways; you can change the strength of the magnetic field, move the conductor in and out of the field, alter the distance between a magnet and the conductor, or change the area of a loop located in a stable magnetic field. No matter how the variation is achieved, the result, an induced current, is the same. The strength of the current will vary in proportion to the change of magnetic flux, as suggested by Faraday’s law of induction. The direction of the current can be determined by considering Lenz’s law, which says that an induced electric current will flow in such a way that it generates a magnetic field that opposes the change in the field that generated it. In other words, if the applied magnetic field is increasing, the current in the wire will flow in such a way that the magnetic field that it generates around the wire will decrease the applied magnetic field. In the above tutorial, a coil of wire connected to an Ammeter is placed in a stable magnetic field; imagine a flux line heading directly into each of the x’s on the board. The area of the coil can be altered by adjusting the Coil Area slider, thus increasing or decreasing the area inside the coil through which the magnetic field is passing. Notice that moving the slider produces an electric current, as shown by the Ammeter; the direction of the current is both reflected in the ammeter reading (positive or negative) and in the black arrows that appear. Notice that the response of the ammeter also varies depending on how quickly you move the coil shape slider. Since the strength of an induced current depends in part on the rate of change in the magnetic flux, changing the coil shape very quickly produces higher readings on the Ammeter than when the coil is adjusted slowly.

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The Letter X In this letter X worksheet, students trace large and small examples of upper and lower case Zaner-Bloser letter Xx. Students also color letter X word pictures. 3 Views 6 Downloads Reinforce young scholars' alphabet skills with a twenty-six page packet featuring the letters of the alphabet. Individual pages focus on one letter, challenge learners to print in upper and lowercase, and copy five words that begin with... K - 1st English Language Arts CCSS: Adaptable Practicing Letters W and X Match initial phonemes to practice recognizing the sounds made by the letters w and x. Early readers circle all of the objects that begin with either an x or a w, then trace each letter several times. Try a fun variation by having... Pre-K - K English Language Arts CCSS: Designed Letter-Sound Match Cut and Paste Develop beginning readers' understanding of letter-sound correspondence with this fun series of cut-and-paste worksheets. With each page focusing on four specific letters, children are able to practice isolating initial sounds as they... 4 mins Pre-K - 1st English Language Arts CCSS: Adaptable Look at Us!: Extra Support Lessons (Theme 1) Support struggling learners and focus on the alphabet with the three weeks of activities and materials provided here. Each day, learners review some letters and practice others in depth. They work on rhyming, practice new words, and... K English Language Arts CCSS: Adaptable

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In the beginning....You may wish to discuss with your children the books that they read. You could ask leading questions such as, Who is the main character? or What important thing happens in the story?. Naturally, the questions that you ask should be relevant to the book. If the book has a moral then you could discuss that or if it is a funny book, then you can talk about what is funny. Discuss the book in present tense, say, "The character is" instead of " The character was". Older children should identify most of the following components of a reading selection. - Important Characters - The Plot - The Setting - The Theme - The Moral - The Mood They could ask themselves: - What is the main idea of the author's story? - Do I agree with the author? Why? - What purpose do I think the author is trying to achieve with this story? - What is the good and what is the evil in this story? or What is the conflict in this story? Book Forms (logs are for 2nd grade and younger) is about, would/would not recommend because) Two (what happened first, next, last, my favorite part) The purpose of a book report: - To acquaint the reader with the book - To give the reader your opinion of the book - To help the reader decide if he/she would like to read the book Although there is no regular form for a book report, there are four parts that a book report should have: - Identify the Book: book title, author's name, and perhaps the publisher, and year of publication - Classify the Book: adventure, fantasy, humor, etc., if it is fact or fiction - Describe the Book: Give an overall view of the book without giving away the outcome. You should include quotes or scenes from the book that you think are representative of the quality (or lack of quality) of the book. - Evaluate the Book: Give your opinion of the book. You can support your opinion with details from the book. You can compare it to other books you've read that are similar. Make your opinion clear!

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Without the ultimate proof of the force behind continental drift, Alfred Wegener’s theory was rejected by most as a fairy tale. The first hint of proof came right after Wegener’s death, with the confirmation of the submerged mountain range called the Mid-Atlantic Ridge under the Atlantic Ocean and a central valley along its crest. Wegener probably would have concluded that this was evidence of the force he was looking for. The mountain range indicated expansion from under the ocean floor, most likely caused by heat, and the valley indicated a stretching of the ocean floor. In the mid-1960s, scientists were able to study Earth’s crust more closely, especially the ocean floor, and discovered that Earth’s outer shell is made up of large, rigid plates that move. The concept is called plate tectonics. We now know that continents and the ocean floor form plates that seem to float on the underlying rock. The underlying rock is under such tremendous heat and pressure that it behaves like a liquid. Wegener said whatever the force was behind continental drift, it would also explain the formation of mountains, earthquakes, volcanoes, and other geological features. The idea of plate tectonics explains all of these. Where plates collide, great mountain ranges are pushed up. If one plate sinks below another, chains of volcanoes are formed. Earthquakes usually form along plate boundaries. Not until the 1960s, after Wegener’s death, was the mechanism of continental drift explained. One year after Wegener died, English geologist Arthur Holmes published his idea that the continents had been “carried” by larger pieces of Earth’s crust. He thought that currents of heat from beneath the crust fueled the movement. His idea was also dismissed until the 1960s. Scientists can now map past plate movements much more precisely than before. Using satellites, they can also measure the speed of continental plate movement. India moves north at a rate of 2 inches per year as it collides with Asia. Current plate movement is also making the Atlantic Ocean larger and the Pacific Ocean smaller by a few inches per year.

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Hydroelectricity is one of the oldest techniques for generating electrical power, with over 150 countries using it as a source for renewable energy. Hydroelectric generators only work efficiently at large scales, though—scales large enough to interrupt river flow and possibly harm local ecosystems. And getting this sort of generation down to where it can power small devices isn't realistic. In recent years, scientists have investigated generating electrical power using nano-structures. In particular, they have looked at generating electricity when ionic fluids—a liquid with charged ions in it—are pushed through a system with a pressure gradient. However, the ability to harvest the generated electricity has been limited because it requires a pressure gradient to drive ionic fluid through a small tube. But scientists have now found that dragging small droplets of salt water on strips of graphene generates electricity without the need for pressure gradients. In their study, published in Nature Nanotechnology, researchers from China grew a layer of graphene and placed a droplet of salt water on it. They then dragged the droplet across the graphene layer at different velocities and found that the process generated a small voltage difference. In addition to being the first to demonstrate this effect, the scientists found a linear relationship between the velocity and the generated electricity. The faster they dragged the droplet across the graphene strip, the higher the voltage they generated. The scientists also found that the voltage increased when multiple droplets of the same size were used at once. What’s the mechanism behind this? The scientists looked at the charge distribution on the sides of the droplet when it was sitting still on graphene, as well as when it was moving. When the droplet was static, the charge redistributed symmetrically on both sides, leaving a net potential difference of zero between them. However, when the droplet was dragged across the graphene strip, this distribution became unbalanced. The scientists found that electrons are desorbed from the graphene at one end of the droplet and are adsorbed into the graphene at another end, which results in a large potential on one side of the droplet and generates a measurable voltage across its length. The scientists then scaled this technology up to demonstrate that you can harvest electricity from it. They used a droplet made of copper chloride and placed it on a graphene surface. The surface was tilted to one side and the droplet was allowed to flow from one end to the other under gravity, resulting in the generation of a measurable voltage—approximately 30mV. Although orders of magnitude lower than today’s hydroelectric generators, these nano-sized generators can work with small devices, something that hydroelectric systems can't do. And they can easily be scaled up, providing the potential to create large-scale generators.

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"Like" us to connect with other students, watch videos, see job offers and even get special discounts. Games in the classroom. Games are an integral part of the Games are an integral part of the learning process. So what is the definition of 'games'' Games are rule-based, and have variable, quantifiable outcomes. Different potential outcomes of a game are assigned different values, some positive and some negative. The player is emotionally attached to the outcome of the game in the sense that the player will be a winner and 'happy' in case of positive outcome, but a loser and 'unhappy' in case of the negative outcome. 'Play' is a free form activity that is often not rule based . Often there are some rules and fixed goals, and time frame, but mostly marked by fluidity of rules and goals.So games are distinguished from play by:- Play is a free ' form activity - Games are rule based, the rules structure the activity and make it possible to repeat it.To prepare a teaching strategy we have to know the age , number , language level and the goals which the students want to achieve .The early childhood stage: 'Play and games' is the most effective form of teaching at the early childhood stage. Children don't see the reason for learning a second language so the teacher has to turn the learning process in to something 'fun' and enjoyable. The teacher has to make use of the natural ability of the child's brain. The children learn by copying than remembering. Children remember visual effects (pictures ) better than the words ,therefore all the games should have a visual help and picture materials. There is also a need for lots of switches and changes with in the game to keep it amusing. Other examples of the games and plays activities are: - Gymnastic and movement games with English commands - Use of music (songs, rhymes) in English- Card games- Role ' plays based on every day situations (in the shop or school) Children age 12 ' 15 years oldThe characteristics of this age are;- independent thinking and working - students are more able to co-work with others The games played at that stage should reach a high level of organization to make the children use there own ideas and an initiative. The games should be orientated on the correct use and the structure of the English language. They should be able practice new words and phrases.- Theme games ( role-play based on scenario )- Listening and singing popular music songs.Young people age 16 ' 22 People at this age are more mature, and intellectually developed. The dominant activity in their life is learning at school/ university so teachers must take advantage of this . Crosswords are the great way of learning at this stage.Mature AgeAn older adult has a very different relation with the games or play activities . They have to convert from real everyday life to the fictional world of games and plays. A child can do it naturally but for an adult it can be difficult. Therefore all kinds of - Strategic games (chess)- Hazard games (poker, roulette) -role-play (an adult can put on the 'mask')- Any kinds of crosswords are appropriate for this age.Use of games and play time is beneficial for students and a teacher because - Fixed goals and rules- Specific climates, beneficial for the student - Creativity - Stimulating, motivating and challenging effects- They are student centered- encourage students to interact and communicate Traditional teaching strategies which view the learner as a means of manipulation rather then an active individual have recently been criticized by psychologist and pedagogies for concentrating too much on the learners' cognitive domain and negligence of the affective one. Recent communicative approach to foreign language teaching / learning process emphasizes the crucial role of individual needs and preferences as to the learning styles. There is need for utilizing materials and activities that originate from the play. The play can be treated as an effective strategy and make the learning process more attractive. References: Teresa Siek ' Piskozub 'Gry I zabawy I symulacje w procesie glottodydaktycznym'

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Although settled without violence, the Nullification Crisis in the 1830s signaled a weakening bond between the states and the federal government, portending the Civil War that ultimately erupted in 1861. Nullification theory took root in American politics much earlier, however, setting the stage for the secession of the Southern states and the establishment of the Confederate States of America. Defining Nullification Theory In his resignation speech to the U.S. Senate, Mississippi Sen. Jefferson Davis said, "Nullification is a remedy which is sought to apply within the Union," further stating that it would serve to preserve the Union when a state believed the federal government had overstepped its authority. John C. Calhoun, vice president under Andrew Jackson, took inspiration from the 1798 Virginia and Kentucky Resolutions when he formulated the idea that a state could declare void, or nullify, any federal law it believed to be unconstitutional. Aggressive and Offensive Taxation In 1828, Congress passed a high tariff designed to protect the interests of American cloth makers. Incensed Southerners decried the "Tariff of Abominations" as unfairly benefitting Northern manufacturers, since the higher tax meant that England bought less of the South's cotton and that finished products were more expensive in the U.S. Tempest in a Southern Tea Pot Calhoun's theory of nullification seemed the perfect answer to Southern consternation over the tariff. Holding to the idea that a state had the right to nullify federal laws within its borders if it found the law to be unconstitutional and injurious to its interests, South Carolina passed an Ordinance of Nullification in 1832, declaring the lower tariff unenforceable in the state. President Jackson believed South Carolina's actions to be treasonous and appealed to Congress for the authority to force the collection of those taxes. Resolving the Immediate Problems In 1833, Congress passed a Force Bill, giving the president the power to use U.S. military to force South Carolina to comply with the federal law. At the same time, the legislature passed the Compromise Tariff of 1833. In response to the compromise tax bill, South Carolina repealed its nullification order but, in a show of temper, passed a bill nullifying the Force Act. Nullification and the Civil War Nullification rights continued to spark passionate debate throughout the next two decades, both over tax bills and attempts to limit the slave trade. When Abraham Lincoln won the presidency in 1860, many factions in the Southern states assumed he would end slavery and make blacks politically and social equal to whites, even though the Republican Party's campaign platform promised no interference with slavery where it already existed. South Carolina again led the charge, using nullification theory to justify its refusal to accept the results of a national election and rallying other Southern states to secede. - U.S. History: 24c. The South Carolina Nullification Controversy - The American Civil War Homepage: Jefferson Davis's Farewell to the U.S. Senate January 21, 1861 - History: Secession - The Gilder Lehrman Institute of American History: The Nullification Crisis - AP Study Notes: Nullification Crisis - United States History: Nullification Crisis - Bill of Rights Institute: Virginia and Kentucky Resolutions (1798) - Ohio State University eHistory Archive: Jackson vs. Calhoun -- Part 2 - Comstock/Stockbyte/Getty Images

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As can be seen from Figure 11.1 the functions printf( ), and scanf( ) fall under the category of formatted console I/O functions. These functions allow us to supply the input in a fixed format and let us obtain the output in the specified form. Let us discuss these functions one by one. We have talked a lot about printf( ), used it regularly, but without having introduced it formally. Well, better late than never. Its general form looks like this... printf ( "format string", list of variables ) ; The format string can contain: (a) Characters that are simply printed as they are (b) Conversion specifications that begin with a % sign (c) Escape sequences that begin with a \ sign For example, look at the following program: int avg = 346 ; float per = 69.2 ; printf ( "Average = %d\nPercentage = %f", avg, per ) ; The output of the program would be... Average = 346 Percentage = 69.200000 How does printf( ) function interpret the contents of the format string. For this it examines the format string from left to right. So long as it doesn’t come across either a % or a \ it continues to dump the characters that it encounters, on to the screen. In this example Average = is dumped on the screen. The moment it comes across a conversion specification in the format string it picks up the first variable in the list of variables and prints its value in the specified format. In this example, the moment %d is met the variable avg is picked up and its value is printed. Similarly, when an escape sequence is met it takes the appropriate action. In this example, the moment \n is met it places the cursor at the beginning of the next line. This process continues till the end of format string is not reached.

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The Equal Concept is derived from the Comparison Concept . It compares two or more fractions, decimals or percentages, etc that represent equal quantities. In this concept, we first draw a model to represent the first variable given and mark out the part of it that will be equal in quantity to a given part in the second variable represented by a second model. To illustrate this concept, consider the following question, 1/4 of A is equal to 1/3 of B. A is greater than B by 40. What is the value of A and B? Step 1: Draw a long bar to represent the whole of A. Divide the bar into 4 equal boxes and label 1 box as the equal part. Step 2: Next, draw a box below the model of A to represent the part of B that is equal to 1/4 of A, i.e., 1/3 of B. Step 3: Since the first box of B drawn represents 1/3 of B, we will need to draw another 2 boxes to its right to represent the remaining 2/3 of B. Step 4: Since A has 4 units and B has 3 units, the extra 1 unit of A must be equal to 40(given in question). 1 unit ----------> 40 3 units ----------> 3 X 40 = 120 4 units ----------> 4 X 40 = 160 Therefore, A is 160 and B is 120. Go To Top - Equal Concept If you want us to send you our future Modelmatics eZine that would inform you on the latest article in Teach Kids Math By Model Method, do an easy sign-up below. Subscription is FREE!

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Title: What Makes A Legend,…A Legend? Grade Level: Fourth of the lesson: 30-40 minutes Overview: This lesson introduces students to the defining characteristics of a legend. Through the use of examples and non-examples, students will be able to distinguish between the story genres of legends, myths, tall tales, and fantasy. Learning Objective: Students will be able to define the characteristics of a legend. Students will be able to distinguish between the characteristics of myths, tall tales, and fantasy stories. Students will be able to explain why a legend is not a myth, tall tale, or fantasy story. Content Standard(s): EL(4) 3. Use a wide range of strategies including distinguishing fiction from nonfiction and making inferences to comprehend fourth-grade recreational reading materials in a variety of genres. EL(4) 4. Identify literary elements and devices, including characters, important details, and similes, in recreational reading materials, and details in informational reading materials. EL(4) 6. Compare the genre characteristics of tall tales, fantasy, myths, and legends, including multicultural literature. Materials and Equipment: One toy plastic shining knight costume, matrices for each student, book examples of legends, tall tales, fantasy stories, and myths, and worksheets Technology Resources Needed: Classroom Smart board and/or computer Background Preparation: Students will already have knowledge on how to define a topics basic characteristics. Students will have also been introduced to legend, myth, tall tale, and fantasy stories. Procedures/Activities: 1. Teacher 1 will engage students by asking for a volunteer. Teacher will then have volunteer put on a toy knight shield and Student will be given a toy sword to hold. The class will be asked to pretend that the shield, helmet, and sword, are real. Class will then be asked to define the characteristics of each piece. Teacher 2 will write class responses on the board. 2. Teacher 1 will read a short excerpt from King Arthur And The Knights Of The Round Table. Students will not know the book title. They will guess what the title is and the kind of story. 3. Teacher 1 will then define the characteristics of a legend. Students will record characteristics on their matrices. 4. Teacher 2 will define the characteristics of myths, tall tales, and fantasy stories. Teacher 1 will write characteristics on the smart board. Students will record characteristics on their 5. Teacher 1 will then engage class in whole group discussion. Teacher 1 will briefly discuss Johnny Appleseed and Rip Van Winkle. Class will be asked if these stories are legends. 6. Teacher 2 will provide other examples for the purpose of understanding which stories are legends and which stories are of another genre. 7. Teacher 2 will give students a worksheet. The worksheet will assess students understanding of legend characteristics. 8. Teacher 1 will conclude by summarizing the defining features of a legend. Assessment Strategies: Students will be given a worksheet. Students will have to identify and write the characteristics of a legend. Time permitting, students will write a short legend. They must include all of a legends’ defining characteristics. Accommodations for Special Ed.: Student A will be asked to be the volunteer for the lesson introduction. Student B will be seated in the front of the classroom. Instructional Model: Guided Discovery Model This lesson defining legend characteristics, will be taught using the Guided Discovery Model. This model focuses on a specific topic and through a series of examples helps to guide students learning to an understanding of that topic. The specific topic of the story genre, legend, is a topic well suited for this model. The topic of the legend has specific defining features/characteristics. Concepts associated with this topic are easily exemplified as well as the ability to provide non-examples. Generalizations will be communicated through the initial introduction of the topic and throughout the lesson. All four phases of the model will be utilized in implementing the lesson. The introduction is described in the above lesson plan. The open-ended phase will include examples and non-examples of the topic. During the convergent phase the students will be questioned and guided to a better understanding of the topic. The closure and application phase of the lesson will incorporate a summary of the definition of the topic. The assessment will consist of a worksheet. Students will demonstrate their understanding of the topic by answering the questions on the worksheet.

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Students solve 3 word problems that use multiplication. They must show their answer in three ways - a picture, repeated addition, and the multiplication equation. They are prompted on the first problem for what the repeated addition and multiplication equation should look like. On the second and third problems, however, they must figure out how to write the repeated addition and multiplication equation on their own. This is great for students getting ready to take Common Core and other state tests. These tests often ask multiplication and division questions by showing pictures or repeated addition/subtraction! This activity works well in stations or centers! See my other multiplication and division worksheets for more practice!

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Rates Of Reaction - Enzymes are biological catalysts. They increase the rate of chemical reactions inside and outside cells. - Enzymes are specific in their action- each enzyme only catalyses a particular chemical reaction or type of chemical reaction. - During digestion, enzymes break down large insoluble food molecules into smaller, soluble ones that can dissolve into blood. How Enzymes Work - This diagram shows how an enzyme works. The substrate binds to a part of the enzyme called the active site. - Notice how they fit together like a lock and key. An enzyme will only catalyse a particular reaction when the shape of its active site matches the shape of the substrate molecule. - The enzyme catalyses the breakdown of the substrate into the products, which then leave the enzyme. The enzyme is then free to join…

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Video solutions to help Grade 7 students learn how to develop rules for multiplying signed numbers. Lesson 11 Student Outcomes Students understand the rules for multiplication of integers and that multiplying the absolute values of integers results in the absolute value of the product. The sign, or absolute value, of the product is positive if the factors have the same sign and negative if they have opposite signs. Students realize that and see that it can be proven to be true mathematically through the use of the distributive property and the additive inverse. Students use the rules for multiplication of signed numbers and give real-world examples. Lesson 11 Summary To multiply signed numbers, multiply the absolute values to get the absolute value of the product. The sign of the product is positive if the factors have the same sign and negative if they have opposite signs. Example 1: Extending Whole Number Multiplication to the Integers Part A: Complete quadrants 1 and 4 of the table below to show how sets of matching integer cards will affect a player’s score in the Integer Game. For example, three 2’s would increase a player’s score by 0 + 2 + 2 + 2 = 6 points. a. What patterns do you see in the right half of the table? b. Enter the missing integers in the left side of the middle row, and describe what they represent. c. What relationships or patterns do you notice between the produtcs (values) in quadrant two and the products (values) in quadrant 1? d. What relationships or patterns do you notice between the products (values) in quadrant two and the products (values) in quadrant four? e. Use what you know about the products (values) in quadrants one, two, and four to describe what quadrant three will look like when its products (values) are entered. f. Is it possible to know the sign of a product of two integers just by knowing in which quadrant each integer is located? Explain. g. Which quadrants contain which values? Describe an integer game scenario represented in each quadrant. Exercise 1: Multiplication of Integers in the Real-World Generate real-world situations that can be modeled by each of the following multiplication problems. Use the Integer Game as a resource. a. -3 × 5 b. -6 × (-3) c. 4 × (-7) This video gives some context clues.

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Lesson 1/Learning Event 2 When the voltage forces the current to flow in a wire, the electrons meet RESISTANCE. Resistance is caused by the friction of the electrons bumping into the atoms. If you rub your fingertips across a table, the friction causes heat. As you move your fingertips faster, the heat becomes greater. Likewise, electrons flowing through a wire cause heat. If the voltage is increased, current flow and the amount of heat are also increased. If the current flow is increased enough, the wire will become hot enough to literally burn up. The heating action of current flow is one of the great uses of electricity. For an example, let's take a look at a light bulb. The bulb contains a filament made of a material that has a lot of resistance to current flow and can withstand extreme heat. The filament ends are connected to two contacts at the base of the bulb. (Usually the metal part of the base serves as one contact.) The filament is then enclosed in glass, and most of the air is removed, because if air gets to the filament, it will burn up too easily. Voltage from a battery or other source is applied to the two contacts at the base of the bulb. Current then flows through the filament causing it to get white-hot which produces light. For the bulb to function properly the material in the filament, the size of the filament, and the amount of voltage supplied must be carefully balanced so just the correct amount of current will flow. If the current flow is too small, the filament will not get heated enough and the bulb will not glow brightly. If the current flow is too great, the filament will burn up. Sometimes a special part known as a RESISTOR is placed in the electrical circuit to reduce the current flow. The action of the resistor can be compared to the restricting action of a water valve or faucet. Opening the valve more will cause more water to flow because there will be less resistance to the flow of water. Likewise, reducing the resistance in an electrical circuit will cause more electrical current to flow. Resistors are usually made from carbon or special wire. Some resistors are "fixed"; that is, they are made so you cannot change the resistance as you can with the faucet in a water system. Resistors that you can adjust are known as "variable" resistors or RHEOSTATS. A rheostat usually has a movable contact that you can move along the length of a resistor. By moving the contact, you change the effective length of the resistor. The greater the distance the current travels to get through the resistor, the greater the resistance of the rheostat.

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Buried deep beneath East Antarctica’s ice sheet, the Gamburtsev Mountains are the world’s most invisible range. New research suggests that overlying ice like that hiding them from view today could have preserved their rugged topography for the past 300 million years. “It’s feasible for topography to be preserved,” says Stephen Cox, a graduate student at Caltech and coauthor of a paper scheduled to appear in Geophysical Research Letters. A supercold cap of ice could have allowed the ancient Gamburtsevs to look like the Alps instead of the highly eroded Appalachians. Russian scientists first identified the Gamburtsevs in 1958 as part of a survey during the International Geophysical Year, and geologists have been puzzled ever since about how the range came to be. The mountains are in a stable part of the continent that hasn’t seen much tectonic activity — usually the way mountains are born — in more than 500 million years. “The Gamburtsevs are either really old, or some big part of the tectonic puzzle is missing,” says Cox. His team tackled the question by looking at how quickly the mountains eroded over time. Because the range is buried, researchers have to study it indirectly — in this case by probing mineral grains at the bottom of Prydz Bay in East Antarctica, where pieces of rock washing off the Gamburtsevs ended up. Grains of the mineral apatite preserve a record, known as a cooling age, of how fast the mountains were eroded. Cox’s team analyzed the apatite in two ways — the amounts of uranium, thorium and helium it contained, and the number of “fission tracks” left by decaying uranium — to build a cooling history of the Gamburtsevs. The team concluded that over the past 250 million years, mountains inland of Prydz Bay eroded just 2.5 to five kilometers — an order of magnitude slower than modern erosion in places like the Alps. Earlier studies had suggested slow Antarctic erosion over the past 118 million years, but the new study takes it farther back in time and supports the idea that the Gamburtsevs really are ancient. Cold glaciers or ice sheets atop the mountains could have protected them from wearing away, Cox suggests. A paper published in Nature last month describes how glaciers could similarly be preserving topography in the southernmost Andes today. “When you get to colder climates, glaciers are actually frozen to the rock,” says geologist Stuart Thomson of the University of Arizona in Tucson, a coauthor of that paper and a member of Cox’s team. “They flow a little, but they don’t erode much at all.” Radar surveys of the Gamburtsevs conducted in 2008 and 2009 confirm that the range is unusually rugged, with V-shaped valleys rather than the U-shaped ones that are characteristic of glacial erosion. Still, another Antarctic expert warns against drawing too many conclusions about ice atop the Gamburtsevs, especially over the past few tens of millions of years. The new work can’t reveal anything explicit about when big ice sheets or smaller mountain glaciers were actually present, says John Goodge, a geologist at the University of Minnesota in Duluth. Yet studying erosion rates could help researchers better figure out the history of Antarctic ice, says Thomson. He is now working on more detailed studies of erosion over the past 34 million years, when the great East Antarctic ice sheet is thought to have started growing. “We’re trying to look at where sediments come from and what they tell us,” he says. Then researchers who use computer models can include those data and see whether current ideas about how Antarctica got icy are correct. Images: 1) Michael Studinger/International Polar Year. 2) Antarctica's Gamburtsev Province Project/IPY.

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What is Magna Carta? Magna Carta is famous as a symbol of justice, fairness, and human rights. For centuries it has inspired and encouraged movements for freedom and constitutional government in Britain and around the world. But when it was issued by England’s King John in June 1215 it was an attempt to prevent a civil war between the king and his powerful barons. Magna Carta means simply ‘great charter’. A charter is a legal document issued by the king or queen which guarantees certain rights. This charter has over 60 clauses, covering many areas of the nation’s life, including the right to a fair trial. It is one of several copies written immediately after King John agreed peace terms with his barons at Runnymede, which were sent around the country as evidence of the king’s decision. Salisbury Cathedral’s copy is one of four which survive from this original issue. It was written in Latin by hand, by an expert scribe, on parchment (animal skin, in this case, sheepskin). Medieval documents like this were not signed, but sealed, and at the bottom of our Magna Carta you can see the marks where King John’s seal was once attached.

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|Nelson EducationSchoolMathematics 1| Surf for More Math Lesson 5 - Exploring 2-D Shapes To encourage students to have fun on the Web while learning about Exploring 2-D Shapes, here are some games and interactive activities they can do on their own or in pairs. Identify 2-D faces of 3-D shapes. Instructions for Use What is a 2-D shape? lets students investigate 2-D shapes. To use What is a 2-D shape?, click on the 2-D shape. Read "What is a 2-D shape?" Click the "Next" button to view the 2-D shapes. Roll over the shapes to see their properties. 2- D Shapes lets students identify the attributes of 2-D shapes. To use 2- D Shapes, answer the question, "What am I?" from the clues given. Click the link answer. Hover over the image to see what it is called.

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On this day in 1809, former President Thomas Jefferson sold John Freeman, an African-American indentured servant, to James Madison, who had recently been sworn in as the nation’s fourth president. At the time, Madison was seeking skilled artisans to work on an extension to his plantation home. Story Continued Below The handwritten contract is now in the Library of Congress. The exhibition notes that Jefferson wrote the agreement on the anniversary of the Battle of Lexington, which launched the American Revolution to end America’s servitude to Great Britain. Jefferson had originally bought Freeman’s services from an unknown source for $400, or about $10,000 in today’s dollars. Madison paid Jefferson an unknown amount. About 77 months were left on Freeman’s 132-month contract, so the sum may have equaled Freeman’s remaining time in service. Like slaves, indentured servants were bought and sold, could not marry without the owner’s permission and were subject to physical punishment. Courts regularly enforced their obligations. But unlike slaves, servants could look forward to being released. When their contracts expired, they were paid “freedom dues” and could live as they pleased. While slaves were primarily of African descent, indentured servants in the post-Revolutionary era were often impoverished white men of European descent, who resorted to selling themselves into servitude in exchange for room and board and sometimes wages. Freeman, a skilled craftsman, was an exception. Relatively few African-Americans in those times became indentured servants. In the nation’s formative years, the practice of indentured servitude was on the wane in favor of “cheaper” slave labor. The Universal Declaration of Human Rights, adopted in 1948, declared indentured servitude illegal. In 2000, Congress implemented its illegality, passing the Trafficking Victims Protection Act. Source: U.S. Library of Congress

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A significant implication is that it is impossible to ever directly observe a black hole from outside the event horizon.* That's right, you will never see a black hole. So, how does one observe a black hole? Thankfully, due to the nature of black holes, scientists have developed several effective methods of observing black holes indirectly, essentially deducing their presence and properties by the black hole's effect on other, observable phenomena. Some of these techniques include: - Gravitational lensing—Strong gravitational fields will cause light (including all electromagnetic radiation) to curve as it passes by a massive object. In a way, the light trapped within a black hole's event horizon is simply light whose path has been curved by gravity to such an extreme that it bends completely back around on itself inside the event horizon. Light passing a great distance from the black hole will be unaffected. But light passing near the black hole will indeed take a curved path, and this curving can be detected by observing objects (such as stars or galaxies) that are out of their expected positions or by noticing multiple images of one object (known as a gravitational mirage). - Accretion discs—Black holes will attract gas particles, which will then form a disc spiraling into the black hole which can be observed directly. Although many cosmic bodies can create an accretion disc, the presence of an accretion disc with no observable center object is indicative of a black hole. - X-rays—As gas is drawn into the black hole from the accretion disc, it will superheat, releasing energy, in particular X-rays, which can be detected. In fact, this is one of the most energy-efficient processes ever observed, transforming up to 40% of the matter to energy. This process occurs just outside the event horizon, enabling the x-rays to escape the black hole's gravitational field. In many cases, the x-rays will be released from electromagnetic poles perpendicular to the accretion disc via relativistic jets (often shown on diagrams of black holes, such as those below). - Black hole binary star systems—In some binary star systems (where two stars orbit around a common point), one of the stars is a black hole which cannot be seen, but its gravitational effect on the companion star can be detected. A famous example is Cygnus X-1. - Gamma ray bursts—These are short bursts of high energy radiation which occur when a large star collapses into a black hole after a supernova, or when two black holes or a black hole and a star collide to form a bigger black hole. - Quasars—Quasars are supermassive black holes at the centers of young galaxies that emit a high volume of x-rays from a large accretion disk. - Gravitational waves—Fluctuations or distortions in space-time are caused by the movements of certain massive objects, including black holes, and those distortions then ripple out from the object. Although the techniques are still experimental, scientists hope to eventually detect black holes by detecting gravitational waves. So, what do black holes have to do with poker? Well, other than the obvious analogy that poker seems to suck all of the interpersonal skills and human decency out of the souls of some players ... Black holes came to mind during my last live poker session because of the concept of indirect detection. I sat down at a 2/5 NLHE table, and there were a few regulars as well as a few players I did not know (which is rather unusual for the Meadows ATM). Two of the regulars are players whose games I respect. One is rather loose preflop, the other is rather tight, but both players are solid postflop players, aggressive when possible, cautious when necessary, but rarely putting chips into the pot without a good reason. Early on, I was fairly card dead, so I wasn't playing a lot of hands. However, by watching the two players I did know, I got a feel for the table. Two of the newbies could be bullied. One was a calling station. Most importantly, there was one newbie with a bigger stack who was given respect by the players I knew. When this newbie played a hand, the regulars showed respect to his bets and raises, and never made moves on him. Clearly, then, two players who I respected felt that this newbie was a solid player and stayed out of his way. So, about an hour into the session, I found AQ on the button. Limped to me, I made a standard raise, solid new guy was the only caller in early position. Flop was A-K-Q rainbow. Yahtzee! New guy checked, I bet 1/2 pot, new guy check-raised for 3x my bet, his standard raise. Now, there are some players who check-raise that flop with any two cards, hoping I have a pocket pair under the board. But given that the regulars respected him, I was worried about the check-raise. A hand that limp-called preflop out of position, then check-raised the flop could easily be something like AK or QQ, possibly JTs. There weren't many hands a tight player would play that way that I could beat. I finally laid it down, deciding there were softer spots at the table. Though I rarely do it, I mucked face up, and the newbie smiled and obligingly showed AK. So, even if you don't have personal history with a player, you can still get a read on him from observing how he interacts with other players, and how other players react to him. Also, a cool way to deal with table d-bags is to throw them into a black hole. * It's also pragmatically impossible to observe a black hole from inside the event horizon, even setting aside the impossibility of ever sending a signal from inside the event horizon to anyone outside the event horizon to describe any observations that might be made. As an observer crossed the event horizon, he would be destroyed as gravitational tidal forces caused spaghettification—essentially, if falling feet first, his feet would be accelerate faster than his head due to stronger gravitational forces, causing his body to be stretched and eventually ripped apart. However, all the observer's matter would eventually join the singularity, which would be a rather cool way to go, if you ever get to pick the way you go.

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