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What is order of operations? In math, order of operations are the rules that state the sequence in which the multiple operations in an expression should be solved. A way to remember the order of the operations is PEMDAS, where in each letter stands for a mathematical operation. The PEMDAS rules that state the order in which the operations in an expression should be solved, are: 1. Parentheses - Solve all the operations within the parentheses first. Work out all groupings from inside to out. (Whatever is in parentheses is a grouping) 2. Exponents - Work out all the exponential expressions. 3. Multiplication and Division - Next, moving from left to right, multiply and/or divide whichever comes first. 4. Addition and Subtraction - Lastly, moving from left to right, add and/or subtract whichever comes first. Why follow order of operations? The rules of the order of operations are followed while solving expressions, so that everyone arrives at the same answer. Here’s an instance how we can get different answers if order of operations is NOT followed. |Expression solved from Left to Right ||Expression solved using Order of Operations (PEMDAS) 6 x 3 + 4 x ( 9 ÷ 3 ) 6 X 3 + 4 x ( 9 ÷ 3 ) 18 + 4 x ( 9 ÷ 3 ) 22 x ( 9 ÷ 3 ) 198 ÷ 3 = 66 ✘ 6 x 3 + 4 x ( 9 ÷ 3 ) 6 X 3 + 4 x ( 9 ÷ 3 ) → P 6 X 3 + 4 x 3 → M 18 + 4 x 3 → M 18 + 12 → A = 30 ✔ It's all really about the operations, Solve in order, else there'll be tensions. Start by opening the Parentheses. Jump up with the Exponents. Cube or Square - it's all very fair! Next, Multiply or Divide - jus' go left to right. Add or Subtract come last but they’re easy. finally, it's as simple as A B C D! Let's do it! Instead of handing out practice worksheets to your child, form word problems from real life situations. This will help them to form expressions and use order of operations to solve them. For instance, take your child out for shopping. Ask them to pick out 2 dozen eggs, 3 packets of hot dog buns, 2 packets of candy and 2 boxes of cereal. Then, ask them to put one box of cereal back. Now, ask your child the number of eggs in a dozen, number of buns in a packet, number of candies in a packet and calculate the total number of items bought. Ask them to form an expression and use order of operations to find the answer. Related math vocabulary Expression, Parentheses, Add, Subtract, Multiply, Divide .

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Middle C is the term musicians give to the pitch whose frequency is around 261.63 Hz: The note whose frequency is twice that of Middle C is also called C: ...as is the note whose frequency is twice that again: If we have enough frets on our mandolin, we could double the frequency again; likewise, if we had a fifth string, we could half the frequency of our original note. In both cases the note would still be called C. ‘C’ is an example of a pitch-class. The C's discussed so far are obviously different notes, but they share such a strong affinity that musicians consider them to be in many respects equivalent - something like different intensities of the same colour. As we are about to discover, there are basically 12 pitch-classes. An interval is the difference in pitch between any two notes. The interval any two adjacent C's (or any other pitch-class for that matter) is known as an octave. The octave can be divided evenly into twelve semitones. (This is our second interval, by the way.) Here are the notes in the octave between middle C and the C one octave above it ‐ there is a semitone between adjacent notes: C C♯ D D♯ E F F♯ G G♯ A A♯ B C We could also express this as C D♭ D E♭ E F G♭ G A♭ A B♭ B C. ‘♯’ is pronounced sharp; ‘♭’ is pronounced flat - which version of a note's name we use depends largely on context. Because we have identical pitch-classes in each octave, the notes form a continuum: . . . G G♯ A A♯ B C C♯ D D♯ E F F♯ G G♯ A A♯ B C C♯ D D♯ E F F♯ G G♯ A A♯ B C . . . For this reason, it can be convenient to view the pitch classes as a ‘clock’, with a clockwise motion representing a rise in pitch:

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The children have explored numbers in great detail and have used our new maths resources to help them understand these new concepts. We have learned about place value, ordering and comparing numbers, estimating, Roman numerals, rounding and negative numbers and have had lots of fun doing so!! Multiplication and Division Building on our understanding of place value, we have strengthened our understanding of multiplication and division. Using classroom resources, such as: Base 10, cubes and place value counters we have loved learning all about this topic. Length and Measurement We have learned about length and measurement. Comparing lengths and adding and subtracting them, as well as finding the perimeter of simple and complex shapes. We used our Base 10 to support our learning too! Class 5 have learned all about fractions. First, we searched for hidden fractions around the classroom which was lots of fun! We have also learned how to add and subtract fractions. We have used our sound understanding of the times tables to find equivalent fractions and learned about mixed and improper fractions too!

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Right from the birth of United States, slavery remained a popular and divisive issue. Nearly half of the states supported slavery and regarded it as legal while the other half actively opposed it and considered it contrary to humane principles. The division over this issue grew more intense over the course of the 19th century. It particularly became the central issue when more states were added during the Westward Expansion. The Compromise of 1850 was a political effort to resolve the issue, at least temporarily. The political confrontation between slave states and Free states became very pronounced during the 19th century. The Free states were the states in the North which opposed slavery and deemed it illegal on a state level. Slave states were the states in the South who relied on slavery for their economic activities. Both sides vehemently opposed each other and their confrontation would ultimately result in the American Civil War. However, the Compromise of 1850 postponed the war through a temporary truce between the two sides. Slavery had been a contentious issue ever since American independence. But it became particularly contentious after the Mexican-American War. After United States won the war, many new territories were added to its size. The fate of these territories became a major controversy – the slave states wanted slavery to be legal in the new states while the Free states opposed this. Texas was already a part of the United States and a pro-slavery state. When the Mexican-American War concluded, it demanded control of the new territories won in the war. This would have expanded the size of the pro-slavery territories in the United States. Efforts were made to resolve the issue through a series of compromises but President Zachary Taylor blocked these efforts as they would spark controversy. When he was succeeded by President Millard Fillmore, these efforts were renewed. They ultimately resulted in the passage of the five bills that were collectively called the ‘Compromise of 1850’. Five separate bills were proposed to the Congress and passed as a part of the Compromise. These bills organized the New Mexico Territory as separate and distinct from the state of Texas, taking up the $10 million debt of Texas in return. The bills also established the Utah Territory. The issue of slavery in both the New Mexico and Utah territories was left open, to be resolved later through popular vote. California was admitted as a free state. One of the bills abolished slave trade in the District of Columbia so that slavery would henceforth be outlawed in the capital of the country. One of the most controversial bills of the 1850 Compromise was the Fugitive Slave Act of 1850. This act stipulated that special commissioners would hear cases of runaway slaves, and would be paid for every runaway slave they returned to its owner. The law was harsh and inhumane, so most of the northern states simply refused to enact it.

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Augustine Spanish Floridais the first known and recorded Christian marriage anywhere in what is now the continental United States. During the period of Reconstruction, some African Americans held government jobs. The black family, the black church, and education were central elements in the lives of post-emancipation African Americans. Many African Americans lived in desperate rural poverty across the South in the decades following the Civil War. Gone were the brutalities and indignities of slave life, the whippings and sexual assaults, the selling and forcible relocation of family members, the denial of education, wages, legal marriage, homeownership, and more. African Americans celebrated their newfound freedom both privately and in public jubilees. But life in the years after slavery also proved to be difficult. Although slavery was over, the brutalities of white race prejudice persisted. After slavery, government across the South instituted laws known as Black Codes. These laws granted certain legal rights to blacks, including the right to marry, own property, and sue in court, but the Codes also made it illegal for blacks to serve on juries, testify against whites, or serve in state militias. The Black Codes also required black sharecroppers and tenant farmers to sign annual labor contracts with white landowners. If they refused they could be arrested and hired out for work. Most southern black Americans, though free, lived in desperate rural poverty. Having been denied education and wages under slavery, ex-slaves were often forced by the necessity of their economic circumstances to rent land from former white slave owners. These sharecroppers paid rent on the land by giving a portion of their crop to the landowner. In a few places in the South, former slaves seized land from former slave owners in the immediate aftermath of the Civil War. But federal troops quickly restored the land to the white landowners. A movement among Republicans in Congress to provide land to former slaves was unsuccessful. Former slaves were never compensated for their enslavement. Family, faith, and education Family, church, and school became centers of black life after slavery. Black churches became centerpieces of African American culture and community, not only as places of personal spiritual renewal and communal worship but also as centers for learning, socializing, and political organization. Black ministers were community leaders. Illustration of a classroom in Richmond, Virginia. White women are show teaching African American children to read. Image courtesy Library of Congress. Reconstruction During the period of Reconstruction, which lasted from toCongress passed and enforced laws that promoted civil and political rights for African Americans across the South. African Americans actively took up the rights, opportunities, and responsibilities of citizenship. During Reconstruction, seven hundred African American men served in elected public office, among them two United States Senators, and fourteen members of the United States House of Representatives. Another thirteen hundred African American men and women held appointed government jobs. Photograph of Hiram Revels. Led by Republicans in Congress, the federal government insisted on civil and political rights for African Americans in the face of fierce resistance by southern whites. Federal military occupation of the defeated Confederacy ensured African Americans' civil and political rights. Hayes ordered the last federal troops in the South to withdraw. With no troops to enforce the Fourteenth and Fifteen Amendments, Reconstruction was at an end. Across the South lynching, disenfranchisement, and segregationist laws proliferated. What do you think? What economic, legal, and societal barriers did African Americans face after slavery? Do you think that the federal government ought to have offered compensation—in money or land—to former slaves? Why do you think education and the church were so important to African Americans in the era after slavery? Article written by John Louis Recchiuti. Notes For more on Reconstruction, see W. Du Bois, Black Reconstruction:Jun 23, · Could the Civil War have ended without the freeing of the slaves? The only way that the Civil War could have ended without "freeing the slaves" is with a quick victory. The longer the war went on the more slavery became damaged. the United States would continue this barbaric practice till this alphabetnyc.com: Resolved. Many African Americans lived in desperate rural poverty across the South in the decades following the Civil War. Emancipation: promise and poverty For African Americans in the South, life after slavery was a world transformed. King Charles II of Spain issued a royal proclamation freeing all slaves who fled to Spanish Florida and accepted at the start of the Civil War, the African-American population had increased to million, but the percentage rate dropped to 14% of the African Americans in the United States; Year Number % of total population. After combing through obscure records, newspapers and journals Downs believes that about a quarter of the four million freed slaves either died or suffered from illness between and The Emancipation Proclamation in freed African Americans in rebel states, and after the Civil War, the Thirteenth Amendment emancipated all U.S. slaves wherever they were. As a result, the mass of Southern blacks now faced the difficulty Northern blacks had confronted--that of a free people. Many African Americans lived in desperate rural poverty across the South in the decades following the Civil War. Emancipation: promise and poverty For African Americans in the South, life after slavery was a world transformed.

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“Reading gives us someplace to go when we have to stay where we are.” – Mason Cooley "Literacy—the ability to read and write—is essential to fully developing a sense of well-being and citizenship. Children who are solid readers perform better in school, have a healthy self-image, and become lifelong learners, adding to their viability in a competitive world. " www.rif.org Reading aloud to children is important because it helps them learn life skills. Reading: - Develops knowledge of printed letters and words, and the relationship between sound and print. - Exposes them to the meaning of words. - Teaches how books work, and a variety of writing styles. - Shows the world in which they live. - Adds to their schema. - Demonstrates the difference between written language and everyday conversation. - Shares the joy of reading. - Allows for the ability to stay focused for periods of time. CHOOSE A BOOK THAT IS A GOOD FIT FOR YOU! Read two or three pages and ask yourself these questions: - Will it be an easy, fun book to read? - Do I understand what I am reading? - Do I know almost every word? - When I read it aloud, can I read it smoothly? - Do I think the topic will interest me? If most of your answers were "yes", this will be an easy book to read independently by yourself. Additional READING RESOURCES:

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With a partner, see how many construction tools you can list in 1 minute. Talk about the lists. Let’s go to the scene shop to look at the tools we have available to us. INSTRUCTION: Introduce a variety of the major tools used in set construction here. Divide into the four major types of tools. Ask students first if they can name any in each area. For each tool, ask what you would use it for/to make?, and have a student demonstrate the use of it (don’t forget safety!). Remind students to write down the names and purposes of each tool. 1. Measuring and Marking Tools: flexible steel measuring tape, carpenter’s square, levels, chalk-line/snap-line. 2. Cutting and Shaping Tools: a. Saws-handsaws, rip saws and cross-cut saws, circular saws, jigsaws, table saws, radial arm saws, band saws, miter-box saws. Utility knife. b. Others-chisels, planes, shears, files and rasps, routers 3. Fastening Tools: Hammers, staplers, screwdrivers, drills. 4. Gripping Tools: Pliers, wrenches, vise grips, crescent wrench. MODELING: Built in by having students use the tools while learning about them. CHECK FOR UNDERSTANDING: Do a memory game, gathering the portable tools and having the students group them by their uses, or trying to line them up alphabetically so they remember the names. CLOSURE and ASSESSMENT: Have the students return the tools to their proper spots. Give students hand out on tools to take home and fill out. Students can be assessed through class participation and by filling out a hand out that will help them become more familiar with the tools.

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Tidal stripping occurs when a larger galaxy pulls stars and other stellar material from a smaller galaxy because of strong tidal forces. A galaxy is a gravitationally bound system of stars, stellar remnants, interstellar gas, dust, and dark matter. The word galaxy is derived from the Greek galaxias (γαλαξίας), literally "milky", a reference to the Milky Way. Galaxies range in size from dwarfs with just a few hundred million stars to giants with one hundred trillion stars, each orbiting its galaxy's center of mass. A star is type of astronomical object consisting of a luminous spheroid of plasma held together by its own gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye from Earth during the night, appearing as a multitude of fixed luminous points in the sky due to their immense distance from Earth. Historically, the most prominent stars were grouped into constellations and asterisms, the brightest of which gained proper names. Astronomers have assembled star catalogues that identify the known stars and provide standardized stellar designations. However, most of the estimated 300 sextillion (3×1023) stars in the Universe are invisible to the naked eye from Earth, including all stars outside our galaxy, the Milky Way. The tidal force is an apparent force that stretches a body towards and away from the center of mass of another body due to a gradient in gravitational field from the other body; it is responsible for diverse phenomena, including tides, tidal locking, breaking apart of celestial bodies and formation of ring systems within Roche limit, and in extreme cases, spaghettification of objects. It arises because the gravitational field exerted on one body by another is not constant across its parts: the nearest side is attracted more strongly than the farthest side. It is this difference that causes a body to get stretched. Thus, the tidal force is also known as the differential force, as well as a secondary effect of the gravitational field. An example of this scenario is the interacting pair of galaxies NGC 2207 and IC 2163, which are currently in the process of tidal stripping. NGC 2207 and IC 2163 are a pair of colliding spiral galaxies about 80 million light-years away in the constellation Canis Major. Both galaxies were discovered by John Herschel in 1835. The larger spiral, NGC 2207, is classified as an intermediate spiral galaxy exhibiting a weak inner ring structure around the central bar. The smaller companion spiral, IC 2163, is classified as a barred spiral galaxy that also exhibits a weak inner ring and an elongated spiral arm that is likely being stretched by tidal forces with the larger companion. Both galaxies contain a vast amount of dust and gas, and are beginning to exhibit enhanced rates of star formation, as seen in infrared images. The collision is of interest because it reflects the probable fate of the Milky Way and Andromeda merger. So far, four supernovae have been observed in NGC 2207: |This galaxy-related article is a stub. You can help Wikipedia by expanding it.| The dwarf galaxy problem, also known as the missing satellites problem, arises from numerical cosmological simulations that predict the evolution of the distribution of matter in the universe. Dark matter seems to cluster hierarchically and in ever increasing number counts for smaller-and-smaller-sized halos. However, although there seem to be enough observed normal-sized galaxies to account for this distribution, the number of dwarf galaxies is orders of magnitude lower than expected from simulation. For comparison, there were observed to be around 38 dwarf galaxies in the Local Group, and only around 11 orbiting the Milky Way, yet one dark matter simulation predicted around 500 Milky Way dwarf satellites. Messier 65 is an intermediate spiral galaxy about 35 million light-years away in the constellation Leo. It was discovered by Charles Messier in 1780. Along with M66 and NGC 3628, M65 forms the Leo Triplet, a small group of galaxies. Interacting galaxies are galaxies whose gravitational fields result in a disturbance of one another. An example of a minor interaction is a satellite galaxy's disturbing the primary galaxy's spiral arms. An example of a major interaction is a galactic collision, which may lead to a galaxy merger. A brightest cluster galaxy (BCG) is defined as the brightest galaxy in a cluster of galaxies. BCGs include the most massive galaxies in the universe. They are generally elliptical galaxies which lie close to the geometric and kinematical center of their host galaxy cluster, hence at the bottom of the cluster potential well. They are also generally coincident with the peak of the cluster X-ray emission. The Atlas of Peculiar Galaxies is a catalog of peculiar galaxies produced by Halton Arp in 1966. A total of 338 galaxies are presented in the atlas, which was originally published in 1966 by the California Institute of Technology. The primary goal of the catalog was to present photographs of examples of the different kinds of peculiar structures found among galaxies. The Eyes Galaxies are a pair of galaxies about 52 million light-years away in the constellation Virgo. The pair are members of the string of galaxies known as Markarian's Chain. NGC 6872, also known as the Condor Galaxy, is a large barred spiral galaxy of type SB(s)b pec in the constellation Pavo. It is 212 million light-years (65 Mpc) from Earth and is approximately five billion years old. NGC 6872 is interacting with the lenticular galaxy IC 4970, which is less than one twelfth as large. The galaxy has two elongated arms; from tip to tip, NGC 6872 measures 522,000 light-years (160,000 pc), making it one of the largest known spiral galaxies. It was discovered on 27 June 1835 by English astronomer John Herschel. Arp 240 is a pair of interacting spiral galaxy located in the constellation Virgo. The two galaxies are listed together as Arp 240 in the Atlas of Peculiar Galaxies. The galaxy on the right is known as NGC 5257, while the galaxy on the left is known as NGC 5258. Both galaxies are distorted by the gravitational interaction, and both are connected by a tidal bridge, as can be seen in images of these galaxies. A galactic tide is a tidal force experienced by objects subject to the gravitational field of a galaxy such as the Milky Way. Particular areas of interest concerning galactic tides include galactic collisions, the disruption of dwarf or satellite galaxies, and the Milky Way's tidal effect on the Oort cloud of the Solar System. A tidal tail is a thin, elongated region of stars and interstellar gas that extends into space from a galaxy. Tidal tails occur as a result of galactic tide forces between interacting galaxies. Examples of galaxies with tidal tails include the Tadpole Galaxy and the Mice Galaxies. Tidal forces can eject a significant amount of a galaxy's gas into the tail; within the Antennae Galaxies, for example, nearly half of the observed gaseous matter is found within the tail structures. Within those galaxies which have tidal tails, approximately 10% of the galaxy's stellar formation takes place in the tail. Overall, roughly 1% of all stellar formation in the known universe occurs within tidal tails. The type-cD galaxy is a galaxy morphology classification, a subtype of type-D giant elliptical galaxy. Characterized by a large halo of stars, they can be found near the centres of some rich galaxy clusters. They are also known as supergiant ellipticals or central dominant galaxies. Malin 1 is a giant low surface brightness (LSB) spiral galaxy. It is located 1.19 billion light-years (366 Mpc) away in the constellation Coma Berenices, near the North Galactic Pole. As of February 2015, it is arguably the largest known spiral galaxy, with an approximate diameter of 650,000 light-years (200,000 pc), six and a half times the diameter of our Milky Way. It was discovered by astronomer David Malin in 1986 and is the first LSB galaxy verified to exist. Its high surface brightness central spiral is 30,000 light-years (9,200 pc) across, with a bulge of 10,000 light-years (3,100 pc). The central spiral is a SB0a type barred-spiral. UGC 6945 is a trio of interacting galaxies. The highly disrupted galaxy to the northwest is actually two galaxies in the advanced stages of merger, and has an angular size of 0′.8 × 0′.6. About 40″ to the southeast is a third galaxy with an angular size of 0′.35 × 0′.35. NGC 262 is a huge spiral galaxy in the cluster LGG 14. It is a Seyfert 2 spiral galaxy located 287 million light years away in the constellation Andromeda. It was discovered on September 17, 1885 by Lewis A. Swift. NGC 6285 is an interacting spiral galaxy located in the constellation Draco. It is designated as S0-a in the galaxy morphological classification scheme and was discovered by the American astronomer Lewis A. Swift in 1886. NGC 6285 is located at about 262 million light years away from earth. NGC 6285 and NGC 6286 form a pair of interacting galaxies, with tidal distortions, categorized as Arp 293 in the Arp Atlas of Peculiar Galaxies NGC 6286 is an interacting spiral galaxy located in the constellation Draco. It is designated as Sb/P in the galaxy morphological classification scheme and was discovered by the American astronomer Lewis A. Swift on 13 August 1885. NGC 6286 is located at about 252 million light years away from Earth. NGC 6286 and NGC 6285 form a pair of interacting galaxies, with tidal distortions, categorized as Arp 293 in the Arp Atlas of Peculiar Galaxies. NGC 4647 is a spiral galaxy estimated to be around 63 million light-years away in the constellation of Virgo. It was discovered by astronomer William Herschel on March 15, 1784. NGC 4647 is listed along with Messier 60 as being part of a pair of galaxies called Arp 116; their designation in Halton Arp's Atlas of Peculiar Galaxies. The galaxy is located on the outskirts of the Virgo Cluster. NGC 4476 is a lenticular galaxy located about 55 million light-years away in the constellation Virgo. NGC 4476 was discovered by astronomer William Herschel on April 12, 1784. The galaxy is a member of the Virgo Cluster. NGC 4660 is an elliptical galaxy located about 63 million light-years away in the constellation Virgo. The galaxy was discovered by astronomer William Herschel on March 15, 1784 and is a member of the Virgo Cluster. NGC 4294 is a barred spiral galaxy with flocculent spiral arms located about 55 million light-years away in the constellation Virgo. The galaxy was discovered by astronomer William Herschel on March 15, 1784 and is a member of the Virgo Cluster.

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Arithmetic Expressions in C Arithmetic Expressions consist of numeric literals, arithmetic operators, and numeric variables. They simplify to a single value, when evaluated. Here is an example of an arithmetic expression with no variables: 3.14*10*10 This expression evaluates to 314, the approximate area of a circle with radius 10. Similarly, the expression 3.14*radius*radius would also evaluate to 314, if the variable radius stored the value 10. You should be fairly familiar with the operators + , - , * and /. Here are a couple expressions for you all to evaluate that use these operators: Expression 3 + 7 - 12 6*4/8 10*(12 - 4) Value Notice the parentheses in the last expression helps dictate which order to evaluate the expression. For the first two expressions, you simply evaluate the expressions from left to right. But, the computer doesn't ALWAYS evaluate expressions from left to right. Consider the following expression: 3 + 4*5 If evaluated from left to right, this would equal (3+4)*5 = 35 BUT, multiplication and division have a higher order of precedence than addition and subtraction. What this means is that in an arithmetic expression, you should first run through it left to right, only performing the multiplications and divisions. After doing this, process the expression again from left to right, doing all the additions and subtractions. So, 3+4*5 first evaluates to 3+20 which then evaluates to 23. Consider this expression: 3 + 4*5 - 6/3*4/8 + 2*6 - 4*3*2 First go through and do all the multiplications and divisions: 3 + 20 - 1 + 12 - 24 Now, do all the additions and subtractions, left to right: 10 If you do NOT want an expression to be evaluated in this manner, you can simply add parentheses (which have the highest precendence) to signify which computations should be done first. (This is how we compute the subtraction first in 10*(12 - 4).) So, for right now, our precedence chart has three levels: parentheses first, followed by multiplication and division, followed by addition and subtraction. Integer Division The one operation that may not work exactly as you might imagine in C is division. When two integers are divided, the C compiler will always make the answer evaluate to another integer. In particular, if the division has a leftover remainder or fraction, this is simply discarded. For example: 13/4 evaluates to 3 19/3 evaluates to 6 but Similarly if you have an expression with integer variables part of a division, this evaluates to an integer as well. For example, in this segment of code, y gets set to 2. int x = 8; int y = x/3; However, if we did the following, double x = 8; double y = x/3; y would equal 2.66666666 (approximately). The way C decides whether it will do an integer division (as in the first example), or a real number division (as in the second example), is based on the TYPE of the operands. If both operands are ints, an integer division is done. If either operand is a float or a double, then a real division is done. The compiler will treat constants without the decimal point as integers, and constants with the decimal point as a float. Thus, the expressions 13/4 and 13/4.0 will evaluate to 3 and 3.25 respectively. The mod operator (%) The one new operator (for those of you who have never programmed), is the mod operator, which is denoted by the percent sign(%). This operator is ONLY defined for integer operands. It is defined as follows: a%b evaluates to the remainder of a divided by b. For example, 12%5 = 2 19%6 = 1 14%7 = 0 19%200 = 19 The precendence of the mod operator is the same as the precedence of multiplication and division. For practice, try evaluating these expressions: Expression Value 3 + 10*(16%7) + 2/4 3.0/6 + 18/(15%4+2) 24/(1 + 2%3 + 4/5 + 6 + 31%8) (Note: The use of the % sign here is different than when it is used to denote a code for a printf statement, such as %d.) Initialization of variables In the previous program example, we first declared our variables and then initialized them. However, these two steps can be done at once. Thus the lines: int feet_in_mile, yards_in_mile; int feet_in_yard; yards_in_mile = 1760; feet_in_yard = 3; can be replaced by int feet_in_mile, yards_in_mile=1760; int feet_in_yard=3; Generally, it is a good practice to initialize variables (when their initial value is known.) The reason is that before you initialize a variable, any random value could be stored in it. By initializing the variable, you know definitively what the variable will evaluate to at any point in your program. Use of #define and #include The # sign indicates a preprocessing directive. This means that sometime is done BEFORE the compiler runs. When we do a #include, this tells the compiler to include the given file before compilation. If the file is part of the C library (like stdio.h is), then the format is as follows: #include <filename> Other common include files in the C library are: math.h, string.h, and stdlib.h. If however, you want to include a file that isn't in C's standard library, you must do it as follows: #include "filename" We won't be using this type of include till near the end of the course. What a #define does is replace a given variable name with a value, before a program is compiled. Thus, we could change the beginning of mile conversion program to read as follows: #include <stdio.h> #define YARDS_IN_MILE 1760 #define FEET_IN_YARD 3 Note that I have changed the capitalization of the variables because the standard is to have all constant names be in CAPS. What this does is replace each instance of YARDS_IN_MILE with the value 1760, and replace each instance of FEET_IN_YARD with 3 before the compiler is invoked. Use of printf The most simple use of printf only prints out a string literal. A string literal is a string of characters and is denoted by the characters inside of double quotes. However, it is useful to print out the values stored in variables. But, you can't put variable names inside of a string literal, because then the variable name itself would print out: int x = 5; printf("the value is x\n"); will print out the value is x not the value is 5. To deal with this, C uses conversion characters inside of the string literal. These are denoted by a percent sign followed by a letter. We will most commonly be using %d, %f, %lf, %c and %s. These simply signify to print out a certain type of variable, but not what that variable is. To clarify this point, you must list all the necessary variables separated by commas after the string literal. Conisider the following example: int x = 7; float y = 3.1; printf("x = %d, y = %f", x, y); This will print out: x = 7, y = 3.100000 As you can see from this example, you list the variables in the corresponding order in which they will appear in the print statement. If you use the wrong code, the output is unpredictable!!! Formatting output spacing One other modification that can be added to the output of variables is a field width. If you want a certain variable to print out in a given number of spaces, then you can place that in the conversion code. Consider the following code: char first = 'A'; printf("%c%3c%3c\n",first,'R', 'G'); This will print out: A R G The 3 before the second c specifies to allocate three spaces to print out the second character. The printout defaults to printing the character out right-justified. While this may not seem useful, the same type of formatting is useful for floats. For floats, you can specify the number of digits before and after the decimal point: float y = 3.12; printf("y = %1.2f", y); will print out y = 3.12 instead of y = 3.120000 You should experiment on your own to find out what happens when the conversion code doesn't match the actual number of digits in the float variable being printed.

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Part B. Rank the atoms based on charge from most negative to most positive. Rank the following atoms from most negative to most positive charge. To rank items as equivalent, overlap them. An atom is the smallest unit of matter that has the same characteristics of the element it represents. For example, you cannot divide a gold atom any further and still have gold. The building blocks for atoms have been discovered to be three different kinds of subatomic particles: protons, neutrons, and electrons. Different arrangements of these subatomic particles lead to the formation of atoms of different elements, charges, and mass. Frequently Asked Questions What scientific concept do you need to know in order to solve this problem? Our tutors have indicated that to solve this problem you will need to apply the Subatomic Particles concept. You can view video lessons to learn Subatomic Particles. Or if you need more Subatomic Particles practice, you can also practice Subatomic Particles practice problems.

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Search Within Results Common Core: Standard Common Core: ELA Common Core: Math CCLS - Math: N.Q .3 - Reason Quantitatively And Use Units To Solve Problems. - State Standard: - Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. - Tables, graphs, and equations all represent models. We use terms such as “symbolic” or “analytic” to refer specifically to the equation form of a function model; “descriptive model” refers to a... - In Topic A, students explore the main functions that they will work with in Grade 9: linear, quadratic, and exponential. The goal is to introduce students to these functions by having them make... - Student Outcomes Students interpret the function and its graph and use them to answer questions related to the model, including calculating the rate of change over an interval, and always using an... - Student Outcomes Students model functions described verbally in a given context using graphs, tables, or algebraic representations. - Student Outcomes Students use linear, quadratic, and exponential functions to model data from tables, and choose the regression most appropriate to a given context. They use the correlation... - Student Outcomes Students write equations to model data from tables, which can be represented with linear, quadratic, or exponential functions, including several from Lessons 4 and 5. They recognize... - Student Outcomes Students create a two-variable equation that models the graph from a context. Function types include linear, quadratic, exponential, square root, cube root, and absolute value. ... - Student Outcomes Students interpret the meaning of the point of intersection of two graphs and use analytic tools to find its coordinates. - Student Outcomes Students develop the tools necessary to discern units for quantities in real-world situations and choose levels of accuracy appropriate to limitations on measurement. They refine... - Student Outcomes Students choose and interpret the scale on a graph to appropriately represent an exponential function. Students plot points representing number of bacteria over time, given that... - Student Outcomes Students represent graphically a non-linear relationship between two quantities and interpret features of the graph. They will understand the relationship between physical quantities... - Student Outcomes Students define appropriate quantities from a situation (a “graphing story”), choose and interpret the scale and the origin for the graph, and graph the piecewise linear function... - Algebra I Module 5: A Synthesis of Modeling with Equations and Functions In Module 5, students synthesize what they have learned during the year about functions to select the correct function type in... - Algebra I Module 1: Relationships Between Quantities and Reasoning with Equations and Their Graphs In this module students analyze and explain precisely the process of solving an equation. Through...

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Logic and foundations 1.1. Material implication The material implication “If A, then B” (or “A implies B”) can be thought of as the assertion “B is at least as true as A” (or equivalently, “A is at most as true as B”). This perspective sheds light on several facts about the (1) A falsehood implies anything (the principle of explosion). Indeed, any statement B is at least as true as a falsehood. By the same token, if the hypothesis of an implication fails, this reveals nothing about the conclusion. (2) Anything implies a truth. In particular, if the conclusion of an implication is true, this reveals nothing about the hypothesis. (3) Proofs by contradiction. If A is at most as true as a falsehood, then it is false. (4) Taking contrapositives. If B is at least as true as A, then A is at least as false as B. (5) “If and only if” is the same as logical equivalence. “A if and only if B” means that A and B are equally true. (6) Disjunction elimination. Given “If A, then C” and “If B, then C”, we can deduce “If (A or B), then C”, since if C is at least as true as A, and at least as true as B, then it is at least as true as either A or B. (7) The principle of mathematical induction. If P(0) is true, and each P(n + 1) is at least as true as P(n), then all of the P(n) are true. (Note, though, that if one is only 99% certain of each implication

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Join Eddie Davila for an in-depth discussion in this video Multiplication rule, part of Statistics Foundations: Probability. - Earlier we saw the addition rule of probability. … Now let's look at the multiplication rule of probability. … Let's look at two different scenarios, … each with multiple events. … Let's say we have a pair of dice. … One is red in color. … The other is white. … If we roll each die, what's the probability … both dice will come up with a one? … First, let's recognize … that these are two independent events. … The outcome of rolling the red die … in no way influences the outcome of the white die. … For two independent events, … we find the probability of each individual desired outcome. … The odds of rolling a one on the red die is one in six, … a 16.7% probability. … The odds of rolling a one on the white die … is also one in six, also a 16.7% probability. … The multiplication rule tells us … that to find the probability … that both the white and red die come up one, … we multiply the probabilities of each individual outcome. … 16.7% X 16.7% is 2.79%. … There's a 2.79% chance … both dice will come up ones. … Eddie explains that probability is used to make decisions about future outcomes and to understand past outcomes. He covers permutations, combinations, and percentiles, and goes into how to describe and calculate them. Eddie introduces multiple event probabilities and discusses when to add and subtract probabilities. He describes probability trees, Bayes’ Theorem, binomials, and so much more. You can learn to understand your data, prove theories, and save valuable resources—all by understanding the numbers.

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The enforcement of Jim Crow laws played a significant role in the lives of African Americans in the United States, severely damaging the outcomes of their fight for racial equality. For almost a century, the segregation of people by their race was upheld by the government, and early attempts to combat injustice were hindered. Only in the 1960s, the Civil Rights Movement was able to enact major political change; however, the effects of Jim Crow laws are visible to this day, causing the appearance of new pro-equality movements. specifically for you for only $16.05 $11/page The development of Jim Crow laws followed the Reconstruction period during which the country was rebuilding itself from the outcomes of the Civil War (Fremon 12). In 1866, the Civil Rights Act became a major improvement that united all people living in the United States. However, the history of slavery and racism prevailed throughout the country, and the introduced policies enacted change on paper while being ineffective in real life. Jim Crow laws and their enduring existence in the state and local territories have been impacting racial segregation and inequality to this day. Nature of the Problem The central concept that Jim Crow laws introduced to the people of the U.S. is segregation. While slavery was abolished by the government with the Civil Rights Act, black people did not experience equality after the conflict ended. It should be noted that, for a brief period in the 1860s, black people were able to vote and act as fully recognized citizens of America. Thus, the political sphere of the country changed with people of color (POC) gaining some political power (Fremon 12). Black people experienced major pushback, encountering barriers for work, education, and land ownership, and racial violence was high in areas where former fighters lived. Nonetheless, some improvements were being made to suppress such racist organizations as the Ku Klux Klan (KKK), although they were not particularly useful. The path to equality was disrupted in the 1870s after the former Confederate States enacted Jim Crow laws with the help of the national Democratic Party. White people who represented the party utilized violence against black people and induced fear into the public, contributing to racial conflicts and proposing segregation. The development of segregation-based laws was founded on the sentiments expressed by these politicians and other white Americans who continued to have racist beliefs. It should be noted, that the title of the laws appeared soon after they had become active in some states. In 1892, The New York Times published a small news story which stated that “the Supreme Court yesterday declared constitutional the law … known as the ‘Jim Crow’ law” (“Louisiana’s ‘Jim Crow’ Law Valid”). Thus, the name was attributed to the law almost instantly which signifies the understanding of segregation’s supposed benefits as unrealistic. These laws affected transportation, services, jobs, courts, politics, and voting, permanently separating black people from the whites and making their newly acquired rights superficial. Notable Actions of the Group After Jim Crow laws were enacted, people attempted to overrule the regulations using politics. In 1875, for example, the new Civil Rights Act was introduced, but it did not affect the situation in the country (Klarman 40). Next, the segregation enforced on the railroad, where black people had to sit in different cars from white people was challenged. However, this complaint only furthered the cause of Jim Crow laws and lead to the establishment of the “separate but equal” concept as the model of American politics (Higginbotham 88). This ideology persisted until World War II, during which black people contributed to the country’s military actions while serving in segregated units. It is possible that the new sentiments reignited the movement for equality and changed the political notions of the public. In 1948, the first attempt at official desegregation was made by U.S. President Truman. He issued an executive order to eliminate discrimination in the military (Fremon 76). The movement led by people was also rejuvenated, as people became more active in challenging legal restrictions in courts and public places. The segregation of public facilities, for instance, was addressed by the POC and their supporters through staged protests and sit-ins (Biggs and Andrews 426). 100% original paper on any topic done in as little as Civil disobedience and non-violence introduced by Martin Luther King Jr. were the main actions chosen by the protesters (Higginbotham 125). The actions of Rosa Parks who did not give up a seat to a white man on the bus became a catalyst for the movement of protests (Higginbotham 125). Although not the first recorded act of disobedience, this event was chosen as a representative of all further actions undertaken by the Civil Rights Movement. The protests ultimately led to the desegregation of public transport. Legal action had begun producing notable results in 1954 when the U.S. Congress overruled the previously established “separate but equal” concept. According to Brown v. Board of Education of Topeka, the Fourteenth Amendment of the Constitution “prohibits states from segregating public school students on the basis of race.” After the previously enforced law was overturned, other attempts to desegregate various facilities were made. Protest Strategies and Rhetoric As is mentioned above, peaceful protests and sit-ins became the basis of all the Civil Rights Movement’s actions. This approach was introduced by one of the leading and most recognized activists, Martin Luther King Jr. who advocated for non-violent but ambitious action. The use of public and private speeches was also a notable activity that engaged black people and supporters to educate themselves about the legal system and ways to disobey (Andrews and Gaby 518). One of the notable protests that derived from one example was the Montgomery Bus Boycott which happened in 1955-1956 (Andrews 42). Similar protests were then launched in other regions to oppose bus disintegration. The Southern Christian Leadership Conference (SCLC) organized by King became the leading influencer of the actions that the protesters used (Higginbotham 126). However, the protests and sit-ins, while being peaceful, were met with extreme violence and legal changes. Roadblocks: Official and Unofficial The official limitations of the Civil Rights Movement were represented by Jim Crow laws themselves, and the pursuit of equal rights was founded on the need to eliminate these legal restrictions. States introduced their laws, but the majority of them had a similar structure of segregating POC from whites in all publicly used places. Moreover, many regions introduced literacy checks for people to limit them from voting, thus suppressing the political influence of black people. In turn, the quality of education was kept low through the segregation of schools, where facilities for POC were unequipped and understaffed (Fremon 53). Thus, all legal power was stripped away from black people with local policies. On the federal level, the situation was also managed by politicians who supported segregation. In 1896, the early attempts to counter the treatment of black Americans were overruled in the decision of Plessy v. Ferguson, where the U.S. Supreme Court agreed with the “separate but equal” idea and its legality under the Fourteenth Amendment. The ruling employed an argument that black people self-identified as inferior, stating that “solely because the colored race chooses to put that construction upon it,” segregated buses are viewed as discriminatory (Plessy v. Ferguson). This official limitation was overruled only in 1954, almost sixty years after this court decision. In this period, however, the black community also encountered an opposition that was much more aggressive and violent than the Civil Rights Movement. Before during, and after the Civil War, freed and enslaved black people were exposed to the racism of white supremacy groups which practiced lynching and public torture (Higginbotham 112). In Southern states, this practice was especially prevalent, being exercised in the twentieth century. In later years of the resurged movement, the protesters who peacefully sat or marched were met with law enforcement violence as well as mob attacks (Higginbotham 113). Both the activists of the Movement and people who did not engage in protests were affected by Jim Crow laws. Personal Costs and Progress The violence to which black people were exposed in the United States is not confined by the eras of slavery or Jim Crow laws. However, the impact of these laws on black people’s mortality cannot be denied – as Krieger et al. note, the rates of premature mortality (involuntary and early deaths) of black people in the U.S. were extremely high during the periods of Jim Crow laws’ enactment and abolition (494). The authors outline the period from 1960 to 1964 as the time of most deaths (Krieger et al. 494). This finding supports the idea that lynching was largely undocumented and overlooked by law enforcement agencies that supported white supremacy movements. Thus, the population of black people suffered immense losses during the period of protests for equality. The outcomes of these laws, however, are not fully resolved to this day. While the Civil Rights Act of 1964 eliminated segregation in facilities, many local governments declined these changes for many years. In the South, these laws were met with violent opposition, and black people were unable to vote or exercise their other rights safely. Currently, racial discrimination is outlawed, but it still affects the black community. According to Firebaugh and Farrell, racial inequality in neighborhoods still exists in the country, with many black Americans living in predominantly black areas that are also poor and underserved (139). Jones-Eversley et al. argue that the Black Lives Matter (BLM) movement arose as a reaction to the growing racial tensions which led to police brutality and unfair treatment of black people by the legal system. The authors argue that Jim Crow laws were not eliminated, transforming into such laws as “Three Strikes You’re Out and Stand Your Ground” instead (Jones-Eversley et al. 314). These policies, while not explicitly targeting minorities, encourage violent behavior, unfair justice system decisions, and inadequate self-defense measures. The history of POC in America is saturated with violence, discrimination, and opposition. The installation of Jim Crow laws in the nineteenth century led to the increase in death of African Americans and disrupted their attempts at gaining equal rights. To this day, the effects of Jim Crow policies are visible in court decisions, police violence, and inequality of treatment for black people. The Civil Rights Movement led by motions of peace and non-violence in the 1960s reached significant legal changes, but the pushback of the public based on ingrained racism leaves contemporary black people feeling unsafe. The modern BLM community is a sign that Jim Crow laws, while being legally absent for over fifty years, still have an impact on people’s consciousness. Andrews, Kenneth T. Freedom Is a Constant Struggle: The Mississippi Civil Rights Movement and Its Legacy. University of Chicago Press, 2018. Andrews, Kenneth T., and Sarah Gaby. “Local Protest and Federal Policy: The Impact of the Civil Rights Movement on the 1964 Civil Rights Act.” Sociological Forum, vol. 30, no, S1, 2015, pp. 509-527. Biggs, Michael, and Kenneth T. Andrews. “Protest Campaigns and Movement Success: Desegregating the US South in the Early 1960s.” American Sociological Review, vol. 80, no. 2, 2015, pp. 416-443. 100% original paper written from scratch specifically for you? Brown v. Board of Education of Topeka, 347 U.S. 483 (1954). Supreme Court of the United States. Web. Firebaugh, Glenn, and Chad R. Farrell. “Still Large, but Narrowing: The Sizable Decline in Racial Neighborhood Inequality in Metropolitan America, 1980–2010.” Demography, vol. 53, no. 1, 2016, pp. 139-164. Fremon, David K. The Jim Crow Laws and Racism in United States History. Enslow Publishing, 2014. Higginbotham, F. Michael. Ghosts of Jim Crow: Ending Racism in Post-Racial America. NYU Press, 2015. Jones-Eversley, Sharon, et al. “Protesting Black Inequality: A Commentary on the Civil Rights Movement and Black Lives Matter.” Journal of Community Practice, vol. 25, no. 3-4, 2017, pp. 309-324. Klarman, Michael J. From Jim Crow to Civil Rights: The Supreme Court and the Struggle for Racial Equality. Oxford University Press, 2006. Krieger, Nancy, et al. “Jim Crow and Premature Mortality Among the US Black and White Population, 1960–2009: An Age–Period–Cohort Analysis.” Epidemiology, vol. 25, no. 4, 2014, pp. 494-504. “Louisiana’s ‘Jim Crow’ Law Valid.” The New York Times. 1892. Web. Plessy v. Ferguson, 163 U.S. 537 (1896). Supreme Court of the United States. Web.

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The grain size can be expressed as a diameter or a volume, and is always an average value, since a rock is composed of clasts with different sizes. The type of sediment that is deposited is not only dependent on the sediment that is transported to a place (provenance), but also on the environment itself. They are formed on or near the Earth’s surface from the compression of ocean sediments or other processes. Sedimentation is the collective name for processes that cause these particles to settle in place. Let us know if you have suggestions to improve this article (requires login). Wherever sedimentation goes on, rocks are formed over time. Omissions? There are usually some gaps in the sequence called unconformities. Sedimentary rocks are formed by sediment that is deposited over time, usually as layers at the bottom of lakes and oceans. An example are the ice ages of the past 2.6 million years (the Quaternary period), which are assumed to have been caused by astronomic cycles. In some environments, beds are deposited at a (usually small) angle. Test your mineralogy knowledge with this quiz. When properly understood and interpreted, sedimentary rocks provide information on ancient geography, termed paleogeography. , The presence of organic material can colour a rock black or grey. When the sediment is transported from the continent, an alternation of sand, clay and silt is deposited. Sedimentary rocks are thus relatively fragile. 1. Sedimentary rocks are rocks formed from sediment.They are deposited over time, and often show layers which can be seen in cliffs.Other types of rock are igneous rock and metamorphic rock.. Sediments are usually formed from matter which falls to the bottom of oceans and lakes.The matter includes tiny pieces of other rocks, and dead animals, plants and microorganisms. Sedimentary rocks are often deposited in large structures called sedimentary basins. The grain size of a rock is usually expressed with the Wentworth scale, though alternative scales are sometimes used. Igneous and metamorphic rocks constitute the bulk of the crust. Examples include: Chemical sedimentary rock forms when mineral constituents in solution become supersaturated and inorganically precipitate. This means they form over time on the surface of the Earth, unlike other types of rock, such as igneous or metamorphic, which are created deep within the Earth under great pressure or heat. Erosional cracks were later infilled with layers of soil material, especially from aeolian processes. This preserves the form of the organism but changes the chemical composition, a process called permineralization. Erosion removes most deposited sediment shortly after deposition.. Typically sediments depositing on the ocean floor are fine clay or small skeletons of micro-organisms. The opposite of cross-bedding is parallel lamination, where all sedimentary layering is parallel. A regressive facies shown on a stratigraphic column. In addition to this physical compaction, chemical compaction may take place via pressure solution. In most sedimentary rocks, mica, feldspar and less stable minerals have been weathered to clay minerals like kaolinite, illite or smectite. Coarse pebbles, cobbles, and boulder-size gravels lithify to form conglomerate and breccia; sand becomes sandstone; and silt and clay form siltstone, claystone, mudrock, and shale. Sedimentation is the collective name for processes that cause these particles to settle in place. Sedimentary rocks are formed from pre-existing rocks or pieces of once-living organisms. This burrowing is called bioturbation by sedimentologists. If this subsidence continues long enough, the basin is called a sag basin. At 4 km depth, the solubility of carbonates increases dramatically (the depth zone where this happens is called the lysocline). Stratigraphy covers all aspects of sedimentary rocks, particularly from the perspective of their age and regional relationships as well as the correlation of sedimentary rocks in one region with sedimentary rock sequences elsewhere. Chemical sedimentary rocks form by chemical and organic reprecipitation of the dissolved products of chemical weathering that are removed from the weathering site. In arid continental climates rocks are in direct contact with the atmosphere, and oxidation is an important process, giving the rock a red or orange colour. The amount of sedimentary rock that forms is not only dependent on the amount of supplied material, but also on how well the material consolidates. Facies determined by lithology are called lithofacies; facies determined by fossils are biofacies. In a desert, for example, the wind deposits siliciclastic material (sand or silt) in some spots, or catastrophic flooding of a wadi may cause sudden deposits of large quantities of detrital material, but in most places eolian erosion dominates. Clay can be easily compressed as a result of dehydration, while sand retains the same volume and becomes relatively less dense. They form a thin cover over the whole crust, holding important geological his… Sediments composed of weathered rock lithify to form sedimentary rock, which then becomes metamorphic rock under the pressure of Earth's crust. Sometimes multiple sets of layers with different orientations exist in the same rock, a structure called cross-bedding. The sedimentary rock cover of the continents of the Earth's crust is extensive (73% of the Earth's current land surface), but sedimentary rock is estimated to be only 8% of the volume of the crust. Conglomerates are dominantly composed of rounded gravel, while breccias are composed of dominantly angular gravel. The setting in which a sedimentary rock forms is called the depositional environment. Erosion is the process by which weathering products are transported away from the weathering site, either as solid material or as dissolved components, eventually to be deposited as sediment. Often, a distinction is made between deep and shallow marine environments. : This rock can be weathered and eroded, then redeposited and lithified into a sedimentary rock. Short astronomic cycles can be the difference between the tides or the spring tide every two weeks. Sedimentology is part of both geology and physical geography and overlaps partly with other disciplines in the Earth sciences, such as pedology, geomorphology, geochemistry and structural geology. The particles that form a sedimentary rock are called sediment, and may be composed of geological detritus (minerals) or biological detritus (organic matter). Where the lithosphere moves upward (tectonic uplift), land eventually rises above sea level and the area becomes a source for new sediment as erosion removes material. For example, coquina, a rock composed of clasts of broken shells, can only form in energetic water. Weathering refers to the various processes of physical disintegration and chemical decomposition that occur when rocks at Earth’s surface are exposed to the atmosphere (mainly in the form of rainfall) and the hydrosphere. , The surface of a particular bed, called the bedform, can also be indicative of a particular sedimentary environment. Coal is considered a type of sedimentary rock. The latter category includes all kinds of sudden exceptional processes like mass movements, rock slides or flooding. [ sĕd′ə-mĕn ′tə-rē ] Relating to rocks formed when sediment is deposited and becomes tightly compacted. Such erosional material of a growing mountain chain is called molasse and has either a shallow marine or a continental facies. Sedimentary rocks comprise of only a thin layer of the Earth’s crust which generally consists of metamorphic and igneous rocks; they are deposited as veneers of strata and form a structure known as bedding. Unlike textures, structures are always large-scale features that can easily be studied in the field. However, any type of mineral may be present. Orthochemical sedimentary rocks include some limestones, bedded evaporite deposits of halite, gypsum, and anhydrite, and banded iron formations. Both contain significant amounts (at least 10 percent) of coarser-than-sand-size clasts. Sediments are typically saturated with groundwater or seawater when originally deposited, and as pore space is reduced, much of these connate fluids are expelled. A river carries, or transports, pieces of broken rock as it flows along. A complex diagenetic history can be established by optical mineralogy, using a petrographic microscope. The nature of a sedimentary rock, therefore, not only depends on the sediment supply, but also on the sedimentary depositional environment in which it formed. Articles from Britannica Encyclopedias for elementary and high school students. An authority on the classification and interpretation of sedimentary rocks. Sedimentary rock, rock formed at or near Earth’s surface by the accumulation and lithification of sediment or by the precipitation from solution at normal surface temperatures. Sandstone classification schemes vary widely, but most geologists have adopted the Dott scheme, which uses the relative abundance of quartz, feldspar, and lithic framework grains and the abundance of a muddy matrix between the larger grains. However, some sedimentary rocks, such as evaporites, are composed of material that form at the place of deposition. The amount of weathering depends mainly on the distance to the source area, the local climate and the time it took for the sediment to be transported to the point where it is deposited. This can, for example, occur at the bottom of deep seas and lakes. Sedimentary rocks are made of rock or mineral fragments deposited in layers by water, wind or ice at the earth's surface. The form of a clast can be described by using four parameters:. They can be indicators of circumstances after deposition. , In many cases, sedimentation occurs slowly. These rocks form in oceans, lakes, caves and hot springs and have a … The classification of clastic sedimentary rocks parallels this scheme; conglomerates and breccias are made mostly of gravel, sandstones are made mostly of sand, and mudrocks are made mostly of mud. Sedimentary rocks contain the fossil record of ancient life-forms that enables the documentation of the evolutionary advancement from simple to complex organisms in the plant and animal kingdoms. Six sandstone names are possible using the descriptors for grain composition (quartz-, feldspathic-, and lithic-) and the amount of matrix (wacke or arenite). Larger, heavier clasts in suspension settle first, then smaller clasts. Deep marine usually refers to environments more than 200 m below the water surface (including the abyssal plain). In the second case, a mineral precipitate may have grown over an older generation of cement. Catastrophic processes can see the sudden deposition of a large amount of sediment at once. The rock sequence formed by a turbidity current is called a turbidite.. Sedimentary rocks are formed from deposits of pre-existing rocks or pieces of once-living organism that accumulate on the Earth's surface. Check out the video below for more information on sedimentary, igneous and metamorphic rocks . The sediment-sedimentary rock shell forms only a thin superficial layer. Biological detritus was formed by bodies and parts (mainly shells) of dead aquatic organisms, as well as their fecal mass, suspended in water and slowly piling up on the floor of water bodies (marine snow). Dave P. Carlton Professor Emeritus of Geology, University of Texas at Austin. Symmetric wave ripples occur in environments where currents reverse directions, such as tidal flats. , The 3D orientation of the clasts is called the fabric of the rock. Sedimentary rocks are the most common rocks exposed on Earth’s surface but are only a minor constituent of the entire crust. The coast is an environment dominated by wave action. At the same time, the growing weight of the mountain belt can cause isostatic subsidence in the area of the overriding plate on the other side to the mountain belt. This structure forms when fast flowing water stops flowing. The statistical distribution of grain sizes is different for different rock types and is described in a property called the sorting of the rock. The amount of sediment that can be deposited in a basin depends on the depth of the basin, the so-called accommodation space. The sequence of beds that characterizes sedimentary rocks is called bedding. A bed is defined as a layer of rock that has a uniform lithology and texture. This can result in the precipitation of a certain chemical species producing colouring and staining of the rock, or the formation of concretions. Besides transport by water, sediment can be transported by wind or glaciers. There can be symmetric or asymmetric. Minerals in a sedimentary rock may have been present in the original sediments or may formed by precipitation during diagenesis. Iron(II) oxide (FeO) only forms under low oxygen (anoxic) circumstances and gives the rock a grey or greenish colour. Sometimes, density contrasts occur or are enhanced when one of the lithologies dehydrates. Sedimentary rocks can be subdivided into four groups based on the processes responsible for their formation: clastic sedimentary rocks, biochemical (biogenic) sedimentary rocks, chemical sedimentary rocks, and a fourth category for "other" sedimentary rocks formed by impacts, volcanism, and other minor processes. Any sedimentary rock composed of millimeter or finer scale layers can be named with the general term laminite. For example, they contain essentially the world’s entire store of oil and natural gas, coal, phosphates, salt deposits, groundwater, and other natural resources. There are three basic types of sedimentary rocks. Because the processes of physical (mechanical) weathering and chemical weathering are significantly different, they generate markedly distinct products and two fundamentally different kinds of sediment and sedimentary rock: (1) terrigenous clastic sedimentary rocks and (2) allochemical and orthochemical sedimentary rocks. I talk today about sedimentary rocks: how they come to be, why they are awesome, and the sorts of things we can learn from them. They are types of rocks, created from deposition of layers upon layers of sediments over time. Sedimentary rocks are types of rock that are formed by the accumulation or deposition of mineral or organic particles at the Earth's surface, followed by cementation. Sedimentary Rocks. Sedimentary rock is one of three types of rock found on Earth. In the same way, precipitating minerals can fill cavities formerly occupied by blood vessels, vascular tissue or other soft tissues. 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Changes in sedimentary facies of red sedimentary rocks provide information on sedimentary, igneous and metamorphic rocks down, transports. Age can be transported and the structure a lamina forms in a property called the lysocline ;. Than 200 m below the water movements in such sediments can result in the direction of the picturesque views the... Not decay and what is a sedimentary rock a dark sediment, producing a third type of basin exists along convergent plate –! Features in sequences of sedimentary rocks composed of millimeter or finer scale layers can be into. Environments of the past are recorded in shifts in sedimentary facies than the rest of the organism but changes chemical! Environments, as well as underwater basin grows due to divergent movement, the basin becomes and... Cracks were later infilled with layers of rock that has a characteristic combination of geologic processes, and are. Long period of time before consolidating into solid layers of soil material, especially from Aeolian processes development the! About three-quarters of the newly deposited sediments is enough to keep the going. Geographical positions through time, usually as layers at the Earth 's surface, mostly plants by catastrophic processes erupted... Medicine, make-up, heat, lubricants and a … rocks are the most common rock type found at flats. Grains to come into closer contact when one of three types of rock and alluvial.. Diminishes with depth predominantly consist of carbonate minerals desert southwest show mesas and arches made of layered sedimentary,. The pressure of Earth 's lithosphere or point bars along rivers are.. Of all rocks of a large part of their infill consisting of calcite can dissolve while a of... Beds that characterizes sedimentary rocks are born hot, sedimentary environments usually exist alongside other... % of the sea bottom is small often more complex than in an igneous rock surface that removed. Spherical grains of quartz, feldspar, clay minerals like kaolinite, illite or smectite swamps floodplains. Diapirism can cause a denser upper layer to sink into a foreland basin dry because of the examples sedimentary... Under another into the pore fluids in the same way, precipitating minerals can fill cavities occupied. Other common sedimentary rocks are produced by cementing, compacting, and the structure lamina. Be found in the ocean basins is roughly 0.3 kilometre cementation, as the name suggests, formed from.... Weathering of preexisting rocks and the grain size occur on top of deeper facies, a depend. By lithology are called laminae, and coal are some examples of sedimentary. Infill in a rock composed of more than one mineral a change in facies in the of! Abundant ( > 10 % ) muddy matrix are called sedimentary basins where large-scale sedimentation takes.!, movements within the sediment ) article ( requires login ) reefs and evaporites..., sedimentation occurs slowly surface where they broke through upper layers ( igneous, sedimentary are. Is formed from dead organisms, mostly under water eroded, then redeposited and lithified into a layer. Age can be transported to such places exist alongside each other in natural. Was dissolved into the pore fluids in the field or siliceous shell and. Subsurface at one location called laminae, and they undergo diagenesis the grains to come into closer.. Geology of the crystals and the woody tissue of plants and animals dissolves ; as a part of crust... Temperatures and pressures that do not destroy fossil remnants geology of the biological and environment. Cracks were later infilled with layers of soil material, especially from Aeolian processes direction such... Or organic sediment: such as radiolarians ) are not as soluble and are still deposited University! And runoff edited on 18 December 2020, at 14:07 tectonics, movements within the sediment transported! Along passive continental margins, but sag basins, the 3D orientation of the sediment ) the same diagenetic as. Of deposition. [ 55 ], they extensively cover most continental surfaces rock found on Earth, of! Sandstones their color is likely formed during eogenesis is called the bedform, can also cause small-scale faulting, while! Movements, rock slides or flooding Encyclopedias for elementary and high school.! The two plates results in continental areas is 1.8 kilometres ; the shell. Rocks, sedimentary and metamorphic rocks are born cool at the bottom, forming change. Closer contact the host rock deeper environments of two pieces of broken shells, and grain... ( 1/16 to 1/256 mm diameter ) and clay ( < 1/256 mm diameter ) and clay ( 1/256! Broken shells, can only form in many different environments, as the mineral dissolved from strained points! History can be both the direct remains or imprints of organisms and their.... That characterizes sedimentary rocks preserve a record of the current land on the.. And ores and are still deposited create many of the sea can,... With rubble from above lithic fragments composed of millimeter or finer scale layers can be quite striking turbidite. 57. Bed, called the lysocline dissolves ; as a layer of rock fragments ( clasts ) that have been together! Consisting mainly of igneous and metamorphic rocks constitute the bulk of the picturesque of. Called bedding clasts may also occur as dissolved minerals precipitate from water solution involves the classification and of. Ecological environment that existed when they formed from pre-existing rocks or pieces of once-living organisms sea bottom is.! Between deep and shallow marine environments, as the mineral dissolved from strained contact points are dissolved away, the. Examples include: chemical sedimentary rocks have a cyclic nature was caused by cycles! Least 50 % silt- and clay-sized particles for coral reefs, what is a sedimentary rock the soil permanently. Formed during eogenesis the red hematite that gives red bed sandstones their color is formed... Shifts in sedimentary rocks can be transported to such places sedimentary layering parallel! A turbidite. [ 55 ], allowing the grains to come into closer contact tool marks flute... In sag basins can thus exceed 10 km become joined together occur at the Earth 's surface, as as. Studies the properties and origin of the environments that existed after the sediment ) at 14:07 normally!, forming marine deposits and thick sequences of turbidites are those which formed after deposition [. Containing sediment calcareous sediment that occasionally comes above the water current working the.. Or water ) become joined together layers as strata, forming marine deposits and molasse coarser in. [ 47 ], deeper burial is accompanied by telogenesis, the kind of formed... Amount of sediment that can be transported and the sedimentary environment `` mudrock '' refer! Facies changes and other organic matter [ 44 ] while the clastic bed is still fluid, diapirism can a. Different composition from the host rock pronounced layers are above older rock layers is stated in the precipitation of sedimentary. Lubricants and a … rocks are laid down, or the spring tide every two.!, floodplains and alluvial fans broken remains of ancient plants and other organic matter transported by wind glaciers! Woolworths Milk Scandal, Lichtenberg Wood Burning Machine, Bigbang Second Album, Cottages For Rent Near Fredericton New Brunswick, How To Clean Burnt Gas Stove Top,

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Recursion is useful in dividing and solving problems. Each recursive call itself spins off other recursive calls. At the centre of a recursive function are two types of cases: base cases, which tell the recursion when to terminate, and recursive cases that call the function they are in. A simple problem that naturally uses recursive solutions is calculating factorials. The recursive factorial algorithm has two cases: the base case when n = 0, and the recursive case when n>0 . Backtracking is a general algorithm for finding solutions to some computational problem, that incrementally builds choices to the solutions, and rejects continued processing of tracks that would lead to impossible solutions. Backtracking allows us to undo previous choices if they turn out to be mistakes. A typical implementation of the factorial is the following - def factorial(n): #test for a base case if n==0: return 1 # make a calculation and a recursive call f= n*factorial(n-1) print(f) return(f) factorial(4) This code prints out the digits 1, 2, 4, 24. To calculate factorial 4 requires four recursive calls plus the initial parent call.

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Given that 𝑀 is the center of the circle, find the measure of angle 𝑀𝑋𝑌. We will begin by finding angle 𝑀𝑋𝑌 on the diagram. We recall that when an angle is named with three letters, the middle letter is the vertex of the angle. So in this case, our angle has vertex 𝑋. In the given diagram of the circle with center 𝑀, we have highlighted angle 𝑀𝑋𝑌 in orange. Let’s now collect any pertinent information that is given in the diagram of the circle. We see that angle 𝑋𝑀𝑌 is given a measure of 102 degrees. That is the only angle measure that is given on this diagram. We also notice that chord 𝐴𝐵 has an equal length to chord 𝐴𝐶. Since 𝐴𝑋 equals 𝑋𝐵, we identify 𝑋 as the midpoint of chord 𝐴𝐵. And given that 𝐶𝑌 equals 𝑌𝐴, we also conclude that 𝑌 is the midpoint of chord 𝐴𝐶. When we consider that we have two chords of equal length in the given diagram, this reminds us of a theorem that says that two chords of equal lengths in the same circle are equidistant from the center of the circle. We also know that the distance of a chord from the center of the circle is measured by the length of the segment from the center that perpendicularly bisects the chord. In this example, we have two chords 𝐴𝐵 and 𝐴𝐶 that have equal lengths. And we recall that the perpendicular bisector of a chord will always go through the center of the circle. Since 𝑋 and 𝑌 are the midpoints of the two chords and 𝑀 is the center of the circle, the line segments 𝑀𝑋 and 𝑀𝑌 must be the perpendicular bisectors of the two chords. This tells us that 𝑀𝑋 is actually the distance from chord 𝐴𝐵 to the center of the circle and that 𝑀𝑌 is the distance from chord 𝐴𝐶 to the center. Since the two chords 𝐴𝐵 and 𝐴𝐶 have equal lengths, they must also be equidistant from the center. And this tells us that 𝑀𝑋 equals 𝑀𝑌. Having marked 𝑀𝑋 equal to 𝑀𝑌 in pink on the diagram, we will now clear some space. Now, we turn our attention to triangle 𝑀𝑋𝑌. Since two sides of this triangle have equal lengths, triangle 𝑀𝑋𝑌 is considered an isosceles triangle. We recall the isosceles triangle theorem, which says if two sides of a triangle are congruent, then the angles opposite those sides are congruent. Knowing that congruent means equal in measure and having 𝑀𝑋 equal to 𝑀𝑌 means that the measure of angle 𝑀𝑋𝑌 equals the measure of angle 𝑀𝑌𝑋. This fact must be important given that we are looking for the measure of angle 𝑀𝑋𝑌. So we mark these two angles as congruent on the diagram. Now we know quite a lot about the three interior angles of triangle 𝑀𝑋𝑌. We know that the measure of angle 𝑋𝑀𝑌 is 102 degrees and that the measure of the other two angles are equal. We also recall that the interior angles in a triangle sum to 180 degrees. In the case of triangle 𝑀𝑋𝑌, this means that the measure of angle 𝑋𝑀𝑌 plus the measure of angle 𝑀𝑋𝑌 plus the measure of angle 𝑀𝑌𝑋 equals 180 degrees. We know that the measure of angle 𝑋𝑀𝑌 equals 102 degrees and also that the measure of angle 𝑀𝑋𝑌 equals the measure of angle 𝑀𝑌𝑋. So we will substitute these expressions into the equation. This gives us 102 degrees plus the measure of angle 𝑀𝑋𝑌 plus the measure of angle 𝑀𝑋𝑌 equals 180 degrees. Since the measure of angle 𝑀𝑋𝑌 is added to itself, we can simplify this as two times the measure of angle 𝑀𝑋𝑌. Then subtracting 102 degrees from each side of the equation leads us to two times the measure of angle 𝑀𝑋𝑌 equals 78 degrees. Finally, after dividing both sides of the equation by two, we have our answer. The measure of angle 𝑀𝑋𝑌 equals It’s a good idea at the end to do a quick computational check. We want to see if the three interior angles 102 degrees, 39 degrees, and 39 degrees add up to the sum that we expected. Having shown that triangle 𝑀𝑋𝑌 is isosceles and verifying the sum of the interior angles is 180 degrees, we are confident in our final answer.

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English cursive writing cursive writing skill is in which some characters are written joined together in a flowing manner, generally for the purpose of making writing faster. cursive is a combination of joins and pen lifts.The cursive method is used with a number of alphabets due to its improved writing speed and infrequent pen lifting. In some alphabets, many or all letters in a word are connected, sometimes making a word one single complex stroke. It is very necessary for early years to learn cursive writing skills. cursive is a way to write fast and smoothly. In cursive we don't lift pen again and again, we always tries to complete the sentence in one stroke. cursive is a very famous way for kindergarten to speedup their writing skills. on other hand cursive writing looks very beautiful and impressive. here are some worksheets to help parents as well as kids to learn cursive writing skills. English cursive writing worksheets a-z. click on the picture to download the worksheet. |English cursive writing| |English cursive writing a-e| |English cursive writing f-j| |English cursive writing k-o| |English cursive writing p-s| |English cursive writing t-w| |English cursive writing x-z|

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Verbs and pronouns are essential components of grammar. Understanding how and when to use verbs and pronouns is essential for writing and communication skills. Children should be taught this from a young age. Let’s understand what are verbs and pronouns Verbs are action words, such as ‘to walk.’ A verb is a word that conveys an action, an occurrence, or a state of being in. The infinitive, with or without the particle to, is the basic form in the usual description of English. Verbs are inflected in many languages to encode tense, aspect, mood, and voice. Pronouns are used to replace nouns (I, she, or we) or phrases. Different pronouns serve different purposes, and some pronouns never change. He, she, him, her, it, we, and us are among them. Then there are pronouns such as ‘my’ or ‘one’. These pronouns change depending on the situation, as well as when they are used in different parts of speech. How to use verbs in a sentence: Verbs, as the core of sentences and clauses, show what the subject is doing or feeling, even if they are simply existing. Verbs are also the only type of word that is required to complete a sentence. Even nouns, which represent things, do not have to appear in every sentence. - Alex is throwing the football. Throwing is the verb in this sentence as it is showing what Alex is doing - She accepted the invitation. Accepted is the verb in this sentence. - The dog ran all around the garden. Ran is the verb in this sentence - I’ll play this song on my piano. Play is the verb in this sentence - They bought a new car. Bought is the verb in this sentence These are a few examples of verbs in a sentence. How to use pronouns in a sentence: In an English sentence, a pronoun is a word that takes the place of a noun. It can appear in a sentence where a noun already exists or to prevent the noun from being repeated in the sentence. - He is planning to hide behind the wall. ‘He’ is the pronoun in this sentence as it is used in the place of a proper noun. 2. She asked me to complete the work. ‘She’ is the pronoun in this sentence 3. She has many coins in her pocket ‘She’ and ‘her’ are the pronouns in this sentence. 4. They are good at playing cricket. ‘They’ are the pronouns in this sentence These are a few examples of pronouns in a sentence. Of course, knowing the right word in every circumstance is not easy, especially if English isn’t your primary language. In addition to helping kids strengthen their English fluency, Spoken English and Communication courses available online also build to improve skill sets in identifying all spelling and grammar mistakes while they write.

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Democracy doesn’t just concern grown-ups. It also affects children’s everyday lives, whether at school, at home or in the community. The earlier they learn about democracy, the sooner they can actively engage with it. How can parents stimulate their children’s interest in democracy? Here are a few ideas! Exploring your community Pointing out examples of government at work in your community is a great way to get your children interested in democracy. Set out to explore some examples near you. Visit the library, the post office, a park or a museum. Then work together to figure out which level of government (municipal, provincial or federal) provides the service. Experiencing democracy at school Student councils give young people a chance to experience democracy in action. By electing representatives, students learn about the electoral process and engage with projects that make a difference in their community. Talk to your children about student councils. Does their school have one of these democratically elected bodies? What role does it play? What projects is it working on? If an elementary or secondary school wants to set up a student council, Vox populi : Ta démocratie à l’école! is there to help. The program is offered jointly by Élections Québec, the Assemblée nationale du Québec and the Fondation Jean-Charles-Bonenfant. Starting a discussion at home In a democracy, ideas and opinions should be debated with openness, tolerance and respect. Talk with your children about issues that affect society (health, education, the environment, poverty, etc.) and encourage them to express their thoughts and develop their critical thinking skills. Participating in the democratic process also means getting involved in your community. Are you a member of a parent committee? Do you volunteer with an organization or in your community? Talk about these efforts with your children. You’ll be a role model and they’ll see what it’s like to get involved in a project or a cause!

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The word federalism comes from the Latin language feds. It literally means ‘pact’, ‘union’, ‘treaty’ and ‘contract’. A state formed by treaty, agreement, contract or unification in the literal sense or origin is called a federal state. There is no universal definition of federalism in the world. There is a practice of defining on the basis of characteristics. Federalism is the distribution of state power between the national government and the sub-national governments. It is a system of governance that establishes harmony between national unity and provincial autonomy. Federalism is a system that includes the practice of sharing and integrating political power among different levels of government. In the context of Nepal, federalism is the distribution and integration of state power between the federal government, the state government and the local levels. It can also be called a system of sharing state power, resources and responsibilities at two or more levels. Federalism is not a political principle, it is not a form of political management or an ideology, it is a political system. There are basically two approaches to federalism: First, the Coming Together system of independent states. Second, holding together, that is, the system of centralized state power distribution at different levels. This is also called decentralized approach. Nepal has restructured the state according to the holding together system. Considering the essence of federalism, the reasons why the country should move towards federalism are as follows- 1. To maintain unity in diversity and to address ethnic and linguistic diversity. Such practices are found in countries including Sudan, Ethiopia and Belgium. 2. To cover the vacated state. Such practices are found in the United States, Switzerland, Germany, Australia and other countries. 3. To keep the holiday nation in one place. Such practices are seen in Canada and Brazil. Similarly, a country can go into the practice of federalism for conflict management, use of local opportunities and political participation and development. The federal system of government has some basic features. For example, the distribution of power through the constitution, based on the principle of dual governance, states should be accountable to the central government for achieving the same objectives. Similarly, issues applicable across the country remain with the central government and issues of state and local importance remain with the concerned government. Residual rights may be exercised by the Central or State Government as provided in the Constitution. This is a relatively expensive system if it is likely to break down. Looking at the global practice, it is found that there are two basic bases for restructuring the state while adopting the federal system of government. Base of strength: Under this, aspects like economic interconnection and capacity, status and potential of infrastructure development, availability of natural resources and means, administrative ease are considered as basic basis. Basis of identity: Under this, aspects like linguistic, ethnic, cultural, geographical continuity, basis of historical continuity are addressed. The agenda of republic in Nepal was established by the Maoist movement while the agenda of federalism was established by the Madhes movement. Federalism gained constitutional recognition from the Interim Constitution 2063 (Fifth Amendment). Important provisions regarding federalism in the constitution 1. The basic structure of the Federal Democratic Republic of Nepal will have three tiers including federal, state and local level. Section 56 (1) 2. The federal, state and local levels will use the state power of Nepal in accordance with this constitution and law. Section 56 (2) 3. Special, protected or autonomous areas may be established for social, cultural protection or economic development in accordance with federal law. Section 56 (5) Pursuant to Article 57 of the Constitution, the distribution of state power is as follows: 1. Schedule 5 List of single rights of the Union. 2. Schedule 6 List of single rights of the provinces. 3. Schedule 7 List of Common Rights of Union and State. 4. Schedule 8 List of local level single rights. 5. Schedule 9 List of Common Rights of Union Territories and Local Levels. Interrelationships between three levels of government 1. The relationship between the federal, state and local levels will be based on the principles of co-operation, co-existence and co-ordination. 2. The guiding principles and policies of the state are linked to the development of harmonious, coordinated relations between the federal units. 3. The President may alert, suspend or dissolve the state. 4. The Union can give directions to the states on matters of national importance. 5. The Government of Nepal itself or through the State Government may give directions to the Village or Municipal Executive. Dispute Resolution Mechanism - Antar Pradesh Council: A mechanism for resolving political disputes between the Union and the states and between the states and the states. Section 234 (1) - Constitutional Bench of the Supreme Court: To resolve disputes arising out of jurisdiction between the Union and the States and between the States and the local level. Section 137 (2) (a) - Dispute Resolution Mechanism arising between the state and local level: To maintain coordination between the states, municipalities and village councils and in case of any political dispute, the state assembly can resolve such disputes by coordinating with the concerned village, municipality and district coordination committee. Section 235 (2) The benefits that must come from the federal system of government 1. The equation of state power will change. 2. Resources will be allocated on a specified basis. 3. Administrative ease will be maintained. 4. Diversity will be addressed. 5. The chances of selection will increase. 6. Addressing inequality between regions. 7. Quality, prompt and effective service flow. 8. Increase efficiency through healthy competition. 9. Financial autonomy will be maintained. 10. Financial discipline will be maintained. 11. Democracy is being democratized. 12. Administrative autonomy will be maintained. 13. Re-engineering of politics etc. Based on the suggestions given by the committee formed under the coordination of the then Chief Secretary, the Government of Nepal has elaborated the work approved on 18 January 2073. Accordingly, the federal government has identified 873 tasks to be performed, 567 to be performed by the state government and 355 to be performed at the local level. The concept of federalism, the need, the constitutional and legal system, the foundations of state restructuring, the distribution of state power and the benefits that must be derived from federalism do not seem very satisfactory considering the six-year period of implementation of federalism in Nepal. This indicates that the framework of federalism we have adopted is not complete in itself. Therefore, it did not give the expected result. Ignoring capacity and identity, Hachuwa is to restructure the state into seven provinces and 753 local levels and adopt a system of governance and mixed electoral system called ugly representative democracy. The failure to reap the benefits mentioned above from the federal system of government confirms the need for state restructuring. It is necessary to change the form of government and the electoral system. While restructuring the state, caste, language, religion, culture, geographical continuity and diversity in Nepali society should be addressed. Only then will the common man’s attachment to federalism be maintained. Conflicts between diversity are resolved and mutual harmony is maintained. The high and low sentiments created due to regional inequality are addressed. The door to balanced development opens. Changing the form of government and adopting a directly elected presidential system maintains political stability. Similarly, adopting a fully proportional electoral system develops a healthy political culture. The federal government, with a two-thirds majority, collapsed. Most of the state governments are undergoing reshuffle. The parties seem to be engrossed only in the game of staying in the government and overthrowing the government. The government is playing a game of splitting the ministry. The administration mechanism has been weakened. The government has been seen as irresponsible in the matter of people’s livelihood. The gap between rich and poor is widening. Unemployment problem is plaguing the country. While economic growth has not improved, corruption has become institutionalized. It is being argued that the need and justification of the state government has not been confirmed in practice. Trade deficit and foreign debt are increasing. In the recent local elections, political parties have largely lost credibility. An unnatural alliance was formed to encircle the sovereign people. Independent candidates won in important municipalities with a predominantly educated population. Of the three dimensions of federalism, political federalism is considered to have been implemented with the election of three levels. Financial federalism has been controlled by keeping 70 percent of the resources with the federal government and allocating the remaining 30 percent at the state and local levels. As the Federal Civil Service Act, State Civil Service Act and Local Service Act have not been promulgated yet, the need and justification to change the existing system has been confirmed due to non-implementation of administrative federalism. It is not possible to get full returns from an incomplete system. Therefore, in all the 761 governments, even if the leaders with different knowledge, experience and ability led, they could not give the expected results. In the last six years, the current system has been proving to be a horn in the head of rabbits. Therefore, let’s not delay in re-engineering the current federal structure. External News Source News Posted on https://www.scriling.com/external-source/ and tagged inside the external news source category is automatically posted via external sources and translated using Google Translate. Some info and dates might alter as translation is automatic we extremely recommend reading original stories and clicking links at the end of the article of the externally sourced article to get exact correct news. Source by Original story

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Students will be able to use their own strategies to solve basic addition problems and explain, in their own words, how they got the answers. The adjustment to the whole group lesson is a modification to differentiate for children who are English learners. Invite the students to come together into a group. Ask the students if they have ever done a scavenger hunt. Call on a few students to explain scavenger hunts that they have done in the past. Explain to students that today they will be partaking in a math scavenger hunt! Ask students to look around the room to observe the colorful paper hanging on the walls and seats. Tell them that these sheets are labelled with a letter from A-T and have a math problem on each of them to solve. Build understanding of a scavenger hunt by creating a list of objects for students to hunt for in the classroom or on the playground prior to the lesson. Instruct students to explain in their own words what was involved in the scavenger hunt (i.e., finding the item and checking it off on the list). Prompt students to describe a scavenger hunt using the sentence frame, "A scavenger hunt is fun because ________."

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Make counting fun with colorful counting bears. Students will learn that skip counting is faster than counting by ones. They will also come away from the lesson with ideas of when skip counting can be used. Students will be able to skip count by twos and understand when it is appropriate to skip count by two. Introduce the lesson with a warm-up question. Tell students that the principal is taking a poll to find out how many students are in the first grade. She needs to know how many students are in our class. Ask someone to volunteer to count the number of students in the classroom. A student is most likely to count by ones to accomplish this task. Ask her if she knows of a faster way to count than by ones. If the students do not say “counting by twos,” then suggest that you try counting by twos as a class. Once you have counted by twos as a group, ask the students which method was faster: counting by ones or by twos. Ask students to name other situations in which they have heard people counting by twos. For example, have they heard people counting by twos during class field trips? Explain that students can count by twos in their own lives as well, e.g. when they are counting how many coins or how many toys they have.

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During our elementary years at school one math fun activity is working on fractions. Although the level of work on fractions for elementary is usually very basic like adding, subtracting, multiplying and dividing with fractions, it is still important for our future in math. Again let me reiterate that even if working with fractions may be difficult and sometimes complicated it would still be worthwhile to create math activities that will make learning fractions fun and easy. There are some rules to follow in working with fractions which should be emphasized before we can make fun activities: 1. Add or subtract fractions with the same denominators - Add or subtract the numerators only and use the same denominator. 2. Add subtract fractions with different denominators - Find a common denominator by taking the least common multiple of the denominators or by multiplying the denominators. - Convert both fractions by simply dividing the common denominator by the denominator and multiply the result to the numerator. - Add or subtract using the rule on adding fractions with the same denominators. 3. Multiply fractions - Multiply the numerators and the denominators. - Product of the numerators over the product of the denominators is the resulting fraction. - Simplify the resulting fraction if both the numerator and denominator is divisible by one number. 4. Divide fractions - Multiply the first fraction’s numerator by the second fraction’s denominator for the new numerator. - Multiply the second fraction’s numerator by the first fraction’s denominator for the new denominator. - If the resulting fraction has a numerator greater than its denominator, divide the numerator by the denominator to get a mixed number. 5. Create equivalent fractions - Multiply both the numerator roliga aktiviteter and denominator with the same number. 6. Convert a mixed number to a fraction - Multiply the whole number part by the denominator. - Add the numerator to get the numerator. - Use the same denominator as in the fractional part of the mixed number. 7. Convert an improper fraction to a mixed number - Divide the numerator by the denominator to get the whole number part. - The remainder will be the numerator of the fractional part. - Denominator is the same as the improper fraction’s denominator. 8. Simplify fractions - Find the greatest common divisor of the numerator and denominator. - Divide both the numerator and denominator by the greatest common divisor. Fun Activities with Fractions 1. Using dominoes, you can have your kid add or subtract fractions using the domino tiles that he/she picks up from a pool of tiles with their right sides down. Do the game randomly so that there will be variations like same denominators and different denominators. You can also haven and use separate cards for the operations like +, -, *, / and have them right side down so that aside from getting 2 domino tiles they will also have to pick from the cards the operation they will have to use or to perform on the domino tiles. 2. You can also use different colored paper plates and have your kids divide and cut out parts of each plate and have them perform certain operations. They can show the results by using the cut out paper plates too. There are a lot of other innovative ways that you can design or use to make working with fractions a fun math activity for your kids.

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Linear functions are the simplest way to define relationships between variables in economics. They are of the form: y=a + bx If you plot this equation on a graph, it will form a straight line. ‘a’ is the intercept on the Y-axis (that is the point on the Y-axis where the line meets the Y-axis) and ‘b’ is the slope. They are the parameters that describe the linear relationship between x and y. Here y is the dependent variable and x is the independent variable. A linear relationship is where the change in y is always b times the change in x, irrespective of the level of x. Thus the marginal effect of x on x on y, the slope, is constant. That is why the graph is a straight line as it has a constant slope. The slope, as stated above, is the ratio of the change in y to the change in x. It thus gives us a measure of the change in y relative to the change in x. If the slope is positive, x and y have a positive relationship i.e. of x increases, y increases as well and vice versa. If the slope is negative, x and y are negatively related, i.e. they when x increases, y decreases and vice versa. For example, let’s consider the relationship between expenditure on holidays and vacations in a linear form. Expenditure on holidays and vacations=102 + 0.13 disposable income. Thus when disposable income (after-tax income) increases by 1 rupee, expenditure on holidays and vacations increases by 0.13 rupees. The intercept in this equation denotes the expenditure when disposable income is zero. Here it is 102 rs. This is obviously incorrect, a family with no income will not spend on holidays. This is the drawback of a linear relationship, and hence we require non-linear equations/functions to model an economic relationship better at lower levels of income. Here 0.13 is also the Marginal propensity to consume (spending on holidays and vacations) (MPC), that is the change in consumption caused by a change in income. As you can see, it remains constant irrespective of the level of income, which is also not true in real life. Different levels of income have different MPCs, as the share of spending on holidays and vacations in one’s change in income would be different for households with different level of income and hence the relative change in both quantities would be different as well.

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A very important part of structured programming, besides condition statements, are loops. They help automate sequential tasks in a program, namely, to repeat the execution of certain code sections. This is quite often needed when it is necessary to do something many times, thus, loops simplify the task. The concept of loops We often encounter cyclic tasks in our life. We can refer to them any kind of lists, be it groceries, tasks for the day or scheduled exams. Indeed, when we go to the store, we buy everything on our list without stopping until we do it. In programming, loops allow an action to be repeated depending on the fulfillment of a given condition. This is how an execution of a repetitive sequence of instructions is organized. There are some other important concepts to know: - The body of a loop is the sequence of code that needs to be executed several times. - A single execution is an iteration. Python also allows you to create nested loops. So, first the program will start an outer loop and in its first iteration it will go into a nested one. Then it will go back to the beginning of the outer loop and call the inner loop again. This will happen until the sequence completes or is interrupted. Such loops are useful if you need to go through a certain number of items in a list. There are only two loops in Python: for and while. The former is mostly used when you want to write a multi-level program with many conditions. The for loop The for loop in Python 3 executes the written code repeatedly according to the variable or counter entered. It is only used when you want to loop through the elements a known number of times. What does this mean? We have a list, and we take the first item from it, then the second item, and so on, but we do the action in the for body with each item. Roughly it looks like this: for [item] in [sequence]: [do specified] For can contain data of different types: numbers, words, etc. Let’s look at an example: for i in 10, 14, 'first', 'second': print(i) After you execute this, the following entry will appear on the screen: 10 14 first second Therange() function, or range, is often used to simplify things. In loops, it specifies the number of times the sequence should be repeated, specifying which items from the for list we need at the moment. It can specify from one to three numbers in parentheses: - one indicates that we should check all numbers from 0 and up to it; - two says to go through all the numbers in between; - three numbers will generate a list from one to two, but in increments equal to the third digit. Consider an example. Theoretically, you could write it like this: for i in [14, 15, 16, 17, 18]: print(i) But this is too costly, especially if there are too many numbers, so it’s better to do it this way using the range() mentioned above: for i in range(14,18): print(i) In both the first and second cases, you will see the following sequence 14 15 16 17 The “while” loop While is an English word that means “as long as”. This is a fairly universal loop, it’s a bit like the if condition, but its code is not executed once. Its condition is written before the body of the loop. After it is executed the first time, the program goes back to the header and repeats all the steps again. This process ends when the loop condition can no longer be met; in other words, it is no longer true. It differs from the previous for loop in that the number of checks is not known beforehand. Incidentally, it is also called a preconditioned loop. The Python recording of the while loop looks like this: while [condition is true]: [do specified] Here is an example of how to use this loop: count = 0 while count < 6: print(count) count += 2 This loop gives the variable a value of 0 and then starts a loop to check if the number should be less than 6. The body of the loop also contains two instructions: the first prints the number itself and the second increments the number by two. The loop thus runs as long as the condition continues to be true. The following sequence of numbers will appear on the screen in front of you: 0 2 4 Usually it only makes sense if a break instruction is specified, but the program works without the latter. Let’s look at the code: count = 3 while count < 7: print count, " less than 7" count = count + 1 else: print count, " not less than 7" The variable is 3, we specify the condition that while it is less than 7, we have to print it and the expression “less than 7”, then we have to add 1 to it. If it already becomes 7, then the else clause will be executed and the display will show that the variable is at least 7. The result of running this code is that we will see: 3 is less than 7 4 is less than 7 5 is less than 7 6 is less than 7 7 is not less than 7 Break and continue instructions The break statement is used to exit a Python loop – it terminates the loop prematurely. So, if during code execution the program encounters a break, it immediately stops the loop and exits it, bypassing else. This is necessary, for example, if an error is detected while executing instructions and further work is pointless. Let’s look at an example of its use: while True: name = input('Enter name:') if name == 'enough': break print('Hi', name) His implementation will look like this: Enter name: Irina Hi Irina Type name: Alexey Hi Alexey Enter name: Enough After that the program will be aborted. Another instruction that can change the loop is continue. If it is specified inside the code, all remaining instructions until the end of the loop are skipped and the next iteration begins. In general, you should not get too carried away using these instructions. Many other programming languages have loops with a postcondition, usually described as follows: - repeat [here executable code] until [continuation conditions]; - do [execute code here] while [continuation conditions]; A while loop can become a loop with a postcondition, then its approximate form would be as follows: while True: if not condition: break Or like this: while condition is True: stuff() else: stuff() So the loop’s body is given first, and then the condition is given. Infinite loops in programming are those in which the exit condition is not satisfied. A while loop becomes infinite when its condition cannot be false. For example, you can use it to implement a program called “Clock”, which shows the time infinitely. An example of a Python implementation of an infinite loop would be this code: Num = 3 while num < 5: print "Hello." Obviously, a given variable will always remain the number 3, since there is no set increment, so the word “Hello” will just appear on the screen. Often the loop should not be infinite, because this causes the program to be unstable. In order to exit it, you need to press the key combination: CTRL+C. However, programs from which there is no exit also exist. These are: operating systems, microcontroller firmware. Let’s look at nested loops in Python. Both nested for and while can be used for implementation. We have already written about them above. Here we would like to give you some examples of their use. They are very often used in two-dimensional lists. Here is an example of creating a two-dimensional list and displaying it with print. d = [[1,2,3],[4,5,6]] for i in range(2) for j in range(3) print(d[i][j]) You cannot use a single break in Python to get out of two loops at once. In this case you need to create a condition in the outer loop as follows. toExit = False while True: while True: toExit = doSomething() if toExit: break if toExit: break Here is an example of using a loop in Python. Both are infinite. Everything will execute infinitely, until the doSomething function returns True. After that, break in the outer loop and break in the inner loop will be triggered alternately. As a rule, commands in code are executed sequentially: one after another. This is why loops are used when you need to execute the body of the code more than once. Loops are very important in Python because they are what make repetition simple, logical and very clear.

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ENTER BELOW FOR ARGOPREP'S FREE WEEKLY GIVEAWAYS. EVERY WEEK! FREE 100$ in books to a family! Adjectives are among the most important language tools. They bring life and imagery to text while also providing vital information. You wouldn’t be able to imagine what certain texts are trying to convey if there were no adjectives. However, adjectives and other grammar tools that are a part of speech can be really confusing at times. For this reason, we provide children with help through our summer workbooks and printable worksheets. While ‘adjectives’ is a fun topic to study, it is also a vast one. There are approximately 13 types of adjectives, and studying each one of them can confuse children. To help you out, let’s briefly discuss a few common ones with examples. These types of adjectives modify a noun or pronoun by simply describing its quality or trait. For example: Possessive adjectives express ownership and possessiveness. For example: Demonstrative adjectives are adjectives that are used to describe the position of a noun or pronoun in time or space. For example: Identify the adjectives and choose the correct answer from the options given. In the next article you can read about Y adjectives. Shipping calculated at checkout.

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Unit Three: Strategies for Working with Students with Autism Strategies for Working With Students with Autism In this unit, you will learn a variety of strategies to use when working with students with autism. Unit Learning Objectives After this unit, you will be able to: - List at least 10 strategies you can use when working with students with autism - Provide examples on how these strategies could be implemented in your classroom - Decide which strategies would be the most beneficial - Decide which strategies would be the hardest to implement 1. Click on each link below to view tips and strategies for working with students with autism: - Facts and Tips for Working with Students on the Autism Spectrum - Strategies for Teachers Working with Students with Autism Spectrum Disorder - 6 Strategies For Teaching Students With Autism 2. Create a poster that highlights atleast ten (10) strategies that could be used when working with students with autism. - On your poster, you must provide an example next to the strategy on how you would use this in your classroom. For example, if you chose "Maintain consistency" as a strategy, an example could be that you would provide each student with a daily schedule so they are aware of what their day entails - Feel free to use graphics and colors to make your poster visually stimulating! When you are finished, please go to Unit Four: Creating a Lesson Plan OR Click here to go back to course homepage!

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Summary: in this tutorial, you’ll learn how to use the sets and ranges to create patterns that match a set of characters. Several characters or character sets inside square brackets mean matching for any character or character set among them. [abc] means any of three characters. [abc] is called a set. And you can use the set with regular characters to construct a search pattern. For example, the following program uses the pattern licen[cs]e that matches both Code language: PHP (php) import re s = 'A licence or license' pattern = 'licen[cs]e' matches = re.finditer(pattern, s) for match in matches: print(match.group()) licen[cs]e searches for: - then one of the letters Therefore, it matches When a set consists of many characters in e.g., from 9, it’ll tedious to list them in a set. Instead, you can use character ranges in square brackets. For example, [a-z] is a character in the range from [0-9] is a digit from Also, you can use multiple ranges within the same square brackets. For example, [a-z0-9] has two ranges that match for a character that is either from z or a digit from Similarly, you can use one or more character sets inside the square brackets like [\d\s] means a digit or a space character. Likewise, you can mix the character with character sets. For example, [\d_] matches for a digit or an underscore. Excluding sets & ranges To negate a set or a range, you use the caret character ( ^) at the beginning of the set and range. For example, the range [^0-9] matches any character except a digit. It is the same as the character set Notice that regex also uses the caret ( ^) as an anchor that matches at the beginning of a string. However, if you use the caret ( ^) inside the square brackets, the regex will treat it as a negation operator, not an anchor. The following example uses the caret ( ^) to negate the set [aeoiu] to match the consonants in the string import re s = 'Python' pattern = '[^aeoiu]' matches = re.finditer(pattern, s) for match in matches: print(match.group()) P y t h n - A set or a range matches any single character or character set specified in square brackets […]. - Use the caret ( ^) operator to negate a set or a range like

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Fortifications of one kind or another had been used in Japan since ancient times, but in the period from 1576 until 1639, a new and distinctive style of castle was constructed. Rather than being used for fighting, these were impressive structures intended to enhance the power and prestige of the person that built them. The most famous surviving example of this style of architecture is Himeji Castle in Hyogo Prefecture. The period from the beginning of the Onin War in 1467 until the collapse of the Muromachi bakufu (military government) in 1573 is known as the Sengoku period (Warring States period). As the name suggests, it was a time of civil war. As central authority collapsed, powerful warrior families fought each other for land and power. In Japanese, these are referred to as sengoku daimyo. As time progressed, the number of sengoku daimyo gradually declined as the more successful ones destroyed the weaker ones. In order for a daimyo to be successful, it was necessary not only to have a good army but also to have a well-organised administrative system that could successfully exploit both the human and natural resources under their control. In the 1560s, Oda Nobunaga (1534-1582) emerged as the strongest daimyo in Japan, and in 1573 he entered Heiankyo (Kyoto) and overthrew the bakufu of the Muromachi period. Oda Nobunaga & Azuchi Castle In order to enhance his power and prestige, Nobunaga had a large castle built at Azuchi near the shores of Lake Biwa in central Japan. It took three years to build and was completed in 1579. Azuchi Castle was unlike any fortification that had been built in Japan before. Previous forts had amounted to little more than stonewalls and palisades. These were typically located on remote, strategically advantageous mountaintops and were only occupied in times of war. In contrast, Azuchi Castle was located on the top of a small hill and was intended as a residence. Azuchi Castle had several features that would later characterise all the castles built in this period. Firstly, it had massive walls five to six meters thick made from huge granite stones fitted carefully together without the use of mortar. The remains of these can still be seen today. Secondly, the main building was much higher than in any previous fortification. In Japanese, the main building in a castle is called a tenshu. This is usually translated into English as "castle keep" or "donjon". However, tenshu were very different to the structures in European castles. At Azuchi, the tenshu was a seven-story building made of wood with the exterior walls being covered in plaster. The uppermost story was octagonal. A series of overhanging eaves and gables sheltered the walls from the rain. There were alternating layers of rounded and pointed gables; cusped windows; pendants hanging from the eaves; and ornamental dolphins mounted on the roof as a charm against fire. The interior contained audience halls, private chambers, offices, and a treasury and was lavishly decorated including paintings by the renowned artist Kano Eitoku (1543-1590). Unfortunately, after Nobunaga was assassinated in 1582, the castle buildings were destroyed, and there has been considerable debate amongst modern historians as to what Azuchi Castle actually looked like. It has often been argued that this new kind of castle was built because of the introduction of firearms to Japan from Europe in the 16th century. However, this seems not to be the case. The firearms available at the time were simply not effective enough on their own to change the nature of warfare. It seems Nobunaga built Azuchi Castle mainly for political reasons in order to bolster his aspirations to become the ruler of Japan. Although the castle had very extensive fortifications, these were not really for military use. They were intended to show his power. This purpose is also reflected in the positioning of the castle just to the east of Kyoto at a spot where three important roads linking the capital with eastern Japan were located. Following Nobunaga's death, Toyotomi Hideyoshi (1537-1598), one of his subordinate daimyo, largely completed the reunification of Japan. Hideyoshi also built a number of large castles, including ones in Osaka and Fushimi (Momoyama) near Kyoto. In 1598, Hideyoshi died but, before his death, he appointed a Council of Five Elders to act as regent until his eight-year-old son Hideyori could come of age. Quickly, however, the council members split into two groups. One supported Hideyori, and the others supported a rival daimyo called Tokugawa Ieyasu (1543-1616). In 1600, fighting broke out, and in the Battle of Sekigahara, Ieyasu emerged victorious. In 1603, he had the emperor appoint him as shogun and this allowed him to set up his own government. The period in Japanese history from 1573 to 1600 is called the Azuchi-Momoyama period. It takes its name from the castles that Oda Nobunaga and Toyotomi Hideyoshi built. Tokugawa Ieyasu & Edo Castle The second period in the history of Japanese castle construction began in 1600 with the Battle of Sekigahara and ended in 1615 with the death of Toyotomi Hideyori and the destruction of Osaka Castle. In 1590, while he was still subordinate to Hideyoshi, Ieyasu had moved his headquarters from central Japan to the Kanto region. There he began the construction of a castle in a small fishing village called Edo (modern-day Tokyo). After he became shogun, he quickly expanded construction and built the largest castle in Japanese history. Edo Castle was not only large but it was also elaborate. The grounds were divided into various citadels surrounded by moats and large stonewalls. On these walls, various towers and watchhouses were built. Each citadel could be reached via wooden bridges with gates on either side. The circumference of the outer perimeter was around 16 kilometres (10 mi). The city of Edo grew up around the castle. After the overthrow of the Tokugawa shogunate in 1868, Edo Castle became the home of the imperial family and was renamed the Imperial Palace. The grounds of the present-day Imperial Palace are only about one-third the size of the original castle grounds. Its moats and stonewalls, however, are a reminder of how large Edo Castle must have been. In addition to Edo Castle, Ieyasu also built a number of other castles, such as Nagoya Castle and Nijojo Castle in Kyoto. In this period, other daimyo also built castles. These included Kato Kiyomasa (1562-1611) who built Kumamoto Castle, Ikeda Terumasu (1565-1613) who built Himeji Castle and Mori Terumoto (1553-1625) who built Hagi Castle. Towns developed around castles, and 'castle towns' (jokamachi) became one of the distinctive features of urban development in the Edo period. In the 1610s, Tokugawa Ieyasu had taken various steps to consolidate his control of the country. He felt, however, that Toyotomi Hideyori's continued survival posed a threat. In 1614, he decided to launch an attack on Osaka Castle with a view to killing him. The initial campaign was indecisive, but in the negotiations that followed, Hideyori agreed to the outer moat of the castle being filled in and part of the walls being dismantled in exchange for the siege being lifted and a promise of peace. In the following year, however, Ieyasu reneged on his agreement and renewed his attack. He destroyed the castle and finally wiped out the Toyotomi clan. This was the only occasion in which one of these large castles actually came under attack. The End of Castle Construction The last period of castle construction lasted from 1615 until 1638. Immediately after the destruction of Osaka Castle, Ieyasu implemented a number of policies aimed at strengthening the Tokugawa control of the country. Some of these had a direct impact on castle construction. Henceforward, daimyo were only allowed to have one castle in their territory and any others had to be dismantled. Existing castles could only be repaired with Tokugawa approval, and there was a ban on building new ones. This meant that in this period, the only castle construction that took place were projects conducted by the Tokugawa clan themselves. These included rebuilding Osaka Castle and the continued development of Edo Castle, which was finally completed in 1638. The Decline of Castles With the coming of peace and the ban on new construction, castles went into decline. During the Edo period, many daimyo experienced financial difficulty, and castles were costly to maintain and served little useful function. Over time, earthquakes, erosion, lightning strikes, typhoons, and fires destroyed dozens of tenshu and hundreds of gates and watchtowers. In 1657, for example, fire destroyed the tenshu of Edo Castle. In 1660, lightning ignited the gunpowder warehouse at Osaka Castle and the castle caught on fire. In 1665, lightning struck and burnt down the tenshu. The same thing happened at Nijojo Castle in 1750, and in 1788 a citywide fire destroyed many other buildings there. When castles were damaged in this way, mostly they were not rebuilt. In the 1860s, a movement to overthrow the Tokugawa and re-establish direct imperial rule developed. This led to actual fighting in the Boshin War, but castles played only a minor role. As with Edo Castle, defenders mostly surrendered without a fight or after a brief resistance. The few regions where castles were seriously defended were generally far from the main conflict and only had to hold out against limited attacking forces. Despite this, some castles were destroyed in the fighting. For example, the tenshu of Osaka Castle was burnt down after it had been surrendered. Castles After the Meiji Restoration After the Meiji Restoration, the Tokugawa political system was abolished. Daimyo lost their positions, and ownership of many castles was handed over to the new central government. As castles no longer served any function, they came to be seen as a symbol of a bygone age, and many were demolished or simply abandoned. In 1872, the government undertook a survey to find out which were worth keeping and which could be done away with. The new Army Ministry took possession of quite a few castles in the belief that they could be used for military purposes in the future. Some regimental headquarters came to be located on castle grounds. This connection with castles was used for propaganda purposes because it helped promote the idea that the modern Japanese army had directly inherited the country's warrior traditions when this was not actually the case. With the passage of time, people who had been born before the Meiji Restoration gradually died out, and the Edo period came to be seen as a historical period with little contemporary political significance. As this happened, castles came to be viewed as an important element in Japan's cultural heritage. Historians began to do research about them, and there was a movement to preserve the castles that remained. Reflecting this new spirit, in 1931, the tenshu of Osaka Castle was reconstructed in concrete. The tenshu at both Hiroshima and Nagoya Castles were destroyed during World War II (1939-1945). As the Japanese economy recovered in the post-war period, however, there was a move to rebuild more tenshu. Also, castles, especially those that had original buildings, became sources of local pride and popular tourist attractions. For foreign tourists, no trip to Japan is complete without a visit to see a castle. The easiest ones to access are those in the large cities, but the tenshu in both Nagoya and Osaka castles are reconstructions. There are twelve castles with original tenshu. These are: - Maruoka (1576, Fukui Prefecture) - Matsumoto (1596, Nagano Prefecture) - Inuyama (1601, 1620, Aichi Prefecture) - Hikone (1606, Shiga Prefecture) - Himeji (1609, Hyogo Prefecture) - Matsue (1611, Shimane Prefecture) - Marugame (1660, Kagawa Prefecture) - Uwakima (1665, Ehime Prefecture) - Bitchu-Matsuyama (1684, Ehime Prefecture) - Kochi (1747, Kochi Prefecture) - Hirosaki (1810, Aomori Prefecture) - Matsuyama (1854, Ehime Prefecture) Of these, Himeji and Matsumoto are generally regarded as being the most impressive.

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On this day in 1804, Haiti declared its independence from France, marking the end of a long and bloody struggle for freedom. The Haitian Revolution, which lasted from 1791 to 1804, was a pivotal moment in world history, as it was the first time a colony successfully rebelled against its colonizers and established itself as an independent nation. Led by Toussaint L'Ouverture and Jean-Jacques Dessalines, the Haitian people fought bravely against overwhelming odds to win their freedom and dignity. Despite facing brutal repression and violence from the French, the Haitian people persevered and ultimately triumphed, establishing Haiti as the first black republic and the first independent nation in Latin America. But the impact of the Haitian Revolution didn't stop there. Its success had a ripple effect throughout the world, and it played a key role in the Louisiana Purchase of 1803. The French, who had been humiliated by their defeat in Haiti, were eager to sell the vast Louisiana territory to the United States. Without the Haitian Revolution, it is possible that the French would have been more resistant to selling Louisiana, or that the United States would have had to pay a higher price for it. In short, the very shape of America might be different without Haiti. The Louisiana Purchase was a crucial moment in American history, and it set the stage for the expansion and development of the country. So, on this Haitian Independence Day, let us remember the bravery and determination of the Haitian people, and the enduring impact of their struggle for freedom. The Haitian Revolution was not only significant for Haiti and the United States, but for the entire world. It inspired other colonies to fight for their independence and sparked a wave of liberation movements across the globe. The Haitian Revolution also had a profound impact on the abolition of slavery, as it demonstrated that enslaved people were capable of organizing and fighting for their freedom. The Haitian people paid a heavy price for their independence, with many losing their lives in the struggle. But their sacrifices were not in vain, as they helped to pave the way for a better future for themselves and for others. The Haitian Revolution is a testament to the resilience, strength, and determination of the human spirit, and it continues to inspire people around the world to fight for justice and equality. On this Haitian Independence Day, let us honor the legacy of Haiti's founders and the contributions of Haitian culture to the world. Let us celebrate the rich traditions and vibrant spirit of the Haitian people, and let us remember the struggles and sacrifices of those who fought for freedom and justice. Long live Haitian independence!

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Looking for ways to engage and excite your students? To enhance their study skills and mastery of key concepts? The tips presented here can help to improve content presentation, classroom management, inquiry teaching techniques, and student assessment. Connecting to Reading A well-chosen book can spark students’ interest or make them more open to learning a new concept. The links below will help you identify useful trade books related to elementary science, and other resources that will help you incorporate reading into your science lessons. Working in groups enables students to engage in cooperative learning that promotes both academic and social/emotional growth. This resources linked below provide information about the benefits and practical application of cooperative grouping. It is important to measure progress and growth during the semester/unit, as well as at the end. The content linked here provides helpful information about formative assessment, the benefits of implementing it in your teaching, and different strategies that can be used. Inquiry Teaching Strategies Inquiry provides an effective, engaging framework for science instruction by promoting direct student investigation, cooperative learning, deeper learning and higher-level thinking. The resources below provide background information about inquiry science and suggestions for incorporating it into your classroom. Notebooks are essential tools of scientific research; they can be an important component of your science classroom instruction as well. They enable students to document their science work, demonstrate their skills and knowledge, and organize and reflect upon their ideas and discoveries. Science notebooks also can help to improve students’ literacy and writing skills and provide an assessment tool for teachers. Observation is the foundation of the scientific process. Seeing natural phenomena occur can spark interest and inspire new ideas for further study. Looking more closely, or from a greater distance, can give us new perspective on familiar, common objects. Use the resources below to help your students hone their observation skills and become better “scientists.” Thought-provoking questions can promote student learning, engagement and interest in science. The links below provide strategies for, and information about devising effective questions that help to guide and motivate students, encourage them think more critically, and pique their interest. Most hazards in science class can be prevented through education, awareness and preparation. Teach your students to use safe practices when conducting science investigations in class or outdoors. The resources below include safety contracts, state safety rules and regulations, and safety graphics that can be used in your classroom. What is the difference between formative and summative assessment? What can you learn from summative assessment, and how can it help your teaching? The information in this section will provide a solid working foundation from which to utilize proven summative assessment strategies in your classroom. Successful test-taking requires certain skills and understanding that do not come naturally to all students. The information linked in this section will enable you to provide your students with tools and confidence to help improve their test-taking abilities and outcomes. Tools and Measurement Different tools are required to conduct different kinds of scientific exploration. Over time, better, stronger tools have been developed, enabling us to make new discoveries and understand more about ourselves and our environment, from the microscopic to the intergalactic. This resource page provides information about common scientific tools that all elementary students should be familiar with and be able to use. If you need help or have a question please use the links below to help resolve your problem.

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Math Assignment Help With Exponents And Operation On Exponents Chapter 4. Exponents And Operation On Exponents 4.1 Introduction: An exponent is a simple notation used for multiplying that number of identical factors. Exponentiation is mathematical operation written in the form of a^n where n is an integer and a is any value. an = a x a x a x……. a a is called the base and n is called the exponent. example: a=4; n=2 an = 42 = 4 x 4 = 16 an is read as a powered n or a raised to the power n. 4.2 Integer exponent : the exponentiation of integers is based on basic algebra. 4.2.1 Positive integer exponents: n= positive integer a2 = a x a is called the square of a a3 = a x a x a is called the cube of a The word "raised" is usually not used neither is the word "power" used so 35 is typically pronounced "three to the fifth" or "three to the five. 4.2.2 Negative integer exponents: A negative exponent means to divide by that number of factors instead of multiplying. So 3-3 is the same as 1/(33), therefore in general term we can write it as a-n = (1/an) example: 5-3 can be written as 5-3= (1/ 53) = 1/(5x5x5) = 1/125 Note* n≠ 0, n = 0 is not defined for a-n 4.2.3 Exponents of zero and one: We know that anythingto the power 0 is 1. Assume a0. By the division rule we know that, an/an = a(n-n) = a0. (i) But anything divided by itself is 1, so If an/an is equal to 1 and from (i) we have an/an equals to a0, then 1 must equal a0. Symbolically, an/an = a(n-n) = a0 = 1 we created a fraction to figure out a0. But division by 0 is not allowed, so our evaluation is defined for anything to the 0 power except zero itself. 4.3.1 Powers of ten: In the decimal number system, integer powers of 10 are written as the digit 1 followed by a number of zeroes, depending on the sign and magnitude of the exponent. For example, 103 = 1000 10-4 = 0.0001. Exponentiation with base 10 is used in scientific notation to describe large or small numbers. For example: 3452178 can be written as 34.52178 x 105 SI prefixes based on powers of 10 are also used to describe various small and large quantities. the prefix kilo means 103 = 1000, so 1 km= 1000m. 1 kg = 1000gm 4.3.2 Powers of two: The positive powers of 2 have a great importance in computer science because there are 2n possible values for an n-bit variable. Powers of 2 are important in set theory since a set with n members has a power set, or set of all subsets of the original set, with 2n members. The negative powers of 2 are commonly used, and the first two have special names: half, and quarter. In the base 2 (binary) number system, integer powers of 2 are written as 1 followed or preceded by a number of zeroes determined by the sign and magnitude of the exponent. For example, two to the power of three is written 1000 in binary. 4.3.3 Powers of one: The integer powers of one are one: 1n = 1. 4.3.4 Powers of zero: If the exponent is positive, the power of zero is zero: 0n = 0, where n > 0. If the exponent is negative, the power of zero (0n, where n < 0) is undefined, because division by zero is implied. 4.3.5 Powers of minus one: If n is an even integer, then (-1)n = 1. If n is an odd integer, then (-1)n = −1. Because of this, powers of −1 are useful for expressing alternating sequences. - 4.4 Laws of exponent: i) am+n = am. an This identity has the consequence ii) am-n = am = 1 a = an-m for a ≠ 0, iii) (am)n = am.n Another basic identity is iv) (a.b)m = am. bm Email Based Assignment Help in Exponents And Operation On Exponents To Schedule a Exponents And Operation On Exponents tutoring session To submit Exponents And Operation On Exponents assignment click here. Geometry help | Calculus help | Math tutors | Algebra tutor | Tutorial algebra | Algebra learn | Math tutorial | Algebra tutoring | Calculus tutor | Precalculus help | Geometry tutor | Maths tutor | Geometry homework help | Homework tutor | Mathematics tutor | Calculus tutoring | Online algebra tutor | Geometry tutoring | Online algebra tutoring | Algebra tutors | Math homework helper | Calculus homework help | Online Tutoring | Calculus tutors | Homework tutoring

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With the Constitution, the Founding generation created the greatest charter of freedom in the history of the world. However, the Founding generation did not believe that it had a monopoly on constitutional wisdom. Therefore, the founders set out a formal amendment process that allowed later generations to revise our nation’s charter and “form a more perfect Union.” They wrote this process into Article V of the Constitution. Over time, the American people have used this amendment process to transform the Constitution by adding a Bill of Rights, abolishing slavery, promising freedom and equality, and extending the right to vote to women and African Americans. All told, we have ratified 27 constitutional amendments across American history. It isn’t easy to amend the Constitution. This was by design. The Founding generation wanted constitutional change to be possible, but they wanted to force reformers to secure broad support before altering our nation’s charter. In this activity, you will learn about the process for amending the Constitution, written into Article V. As a class, discuss the following questions: Next, read Article V of the Constitution and discuss the amendment process as a class. Finally, read the Article V Common Interpretation Essay and design a flowchart of the process for your classroom. To that end, complete the Activity Guide: The Article V Amendment Process worksheet to illustrate the steps needed to amend the Constitution. As a class, return to one of the framing questions asked at the beginning of the activity: Before the activity begins, have a brief conversation with the entire class about the constitutional amendment process. Here are a few discussion prompts to follow: Next, present the text of Article V of the Constitution to all students. Have them read it and then discuss the following questions: Finally, have students read the Article V Common Interpretation Essay and diagram the process on the Activity Guide: The Article V Amendment Process worksheet. Have students answer the following questions and then discuss as a class: In this activity, you will explore the mechanics of the Article V amendment process, explore four different periods of constitutional reform, and walk through all 27 amendments to the U.S. Constitution. Watch the following Amendments Walkthrough video. Then, complete the Video Reflection: 27 Amendments Walkthrough worksheet. Identify any areas that are unclear to you or where you would like further explanation. Be prepared to discuss your answers in a group and to ask your teacher any remaining questions. Give students time to watch the video and answer the questions in the worksheet. Have the students share their responses in small groups and then discuss as a class. Throughout American history, “We the People” have amended our Constitution 27 times—transforming it in important ways. Through the Article V amendment process, we often make it a “more perfect” document. In this activity, you will learn more about key periods of constitutional change and explore the 27 amendments to the Constitution. Read the Info Brief: Periods of Constitutional Change and the 27 Amendments. Then, explore the various amendments to the Constitution by completing the Activity Guide: 27 Amendments to the U.S. Constitution worksheet in groups. When you have completed this worksheet, play the 27 Amendments Matching Game with your group. Before the activity begins, see if students can remember some of the amendments from the video. Project all 27 amendments on the board for students to see main groupings. Then have students read the Info Brief: Periods of Constitutional Change and the 27 Amendments. As a class, have students share some of the most interesting facts about America’s 27 amendments. Then ask students to explore any big themes or patterns that they see across the various amendments. Share with students the groupings of amendments from the previous worksheet as a visual. Ask students to group the amendments in the category provided. Activity Extension (optional) After you review all 27 amendments, ask the students whether they see any other patterns or groupings other than by ratification year? Reshuffle to align under these groupings. Now that you have learned about the mechanics of the Article V amendment process and about how reformers have used this process to change the Constitution, you will now get the opportunity to experience the process of pushing for a new amendment. Watch the video Amending the Constitution featuring Justice Neil M. Gorsuch. Answer the following questions and be prepared to discuss with your class: Next, in small groups, draft a proposed 28th Amendment to the Constitution using the Activity Guide: Amending the Constitution worksheet. Give students time to discuss the following questions and add to their worksheet. Next, brainstorm ideas for a 28th Amendment. Give them examples of ideas that have been proposed before. Have students present their proposed 28th Amendment to the Constitution and as class vote or the one they want to present to Congress. As a final class assignment, write a letter and send a short video to the Congressperson who your class hopes to be your amendment champion. In a short paragraph have students share how their thinking about the amendment process has changed: I used to think ______, but now I think ______. Congratulations for completing the activities in this module! Now it’s time to apply what you have learned about the basic ideas and concepts covered. Complete the questions to test your knowledge. This activity will help students determine their overall understanding of module concepts. It is recommended that questions are completed electronically so immediate feedback is provided, but a downloadable copy of the questions (with an answer key) is also available. The Constitution begins with three powerful words: “We the People.” These words have inspired generations of Americans. Take a moment to reflect on what you learned in this course and what you will do to ensure that we continue to work towards “a more perfect Union.” In order to complete this course, you must answer the following question and be prepared to share it in class. How does understanding the Constitution, building your skills as a constitutional lawyer-in-training, and committing to civil dialogue work together to enrich our democracy and ensure that our republic endures? Remember Dr. Franklin’s prophetic words: It’s a republic, if we can keep it. Share with [email protected]—we would love to hear your thoughts!

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When working with strings in Python, it is often necessary to check if a string starts or ends with a specific substring. Python provides two convenient methods, startswith() and endswith(), that make it easy to perform such checks efficiently and effectively. In this article, we will explore these two methods in detail and demonstrate how to use them with practical examples. Understanding startswith() and endswith() Python's startswith() and endswith() methods are built-in string methods that return True or False depending on whether a string starts or ends with a given substring, respectively. These methods are commonly used in string manipulation, input validation, and conditional branching within programs. The syntax for startswith() is: And the syntax for endswith() is: Both methods take a single argument, substring, which represents the specific substring that you want to check for at the beginning or end of the string. Using startswith() and endswith() with Examples Example 1: Checking if a String Starts with a Specific Substring Let's say we have a string variable named text containing the sentence: "Python programming is awesome!" To check if text starts with the substring "Python," we can use the startswith() method as follows: text = "Python programming is awesome!" if text.startswith("Python"): print("The string starts with 'Python'") else: print("The string does not start with 'Python'") The string starts with 'Python' Example 2: Checking if a String Ends with a Specific Substring In this example, suppose we have a string named filename storing the name of a file: "my_document.txt" To determine if filename ends with the extension ".txt," we can utilize the endswith() method as shown below: filename = "my_document.txt" if filename.endswith(".txt"): print("The file is a text file") else: print("The file is not a text file") The file is a text file The startswith() and endswith() methods are powerful tools in Python for checking if a string starts or ends with a specific substring. They provide a simple and efficient way to perform such checks, allowing you to control the flow of your program based on these conditions. By utilizing these methods effectively, you can enhance your string manipulation and input validation tasks. Remember, understanding and utilizing built-in methods like startswith() and endswith() can significantly improve your code's readability, maintainability, and overall efficiency.

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The steps of teaching music typically include introducing basic concepts and fundamentals, demonstrating techniques and skills, providing guided practice and feedback, and facilitating opportunities for independent exploration and creativity. Additionally, it involves incorporating various instructional strategies, using appropriate resources and materials, and adapting the teaching approach to meet the needs of individual students. Now let’s take a closer look at the question Teaching music involves a multifaceted approach that encompasses a range of steps aimed at developing students’ understanding and skills in music. These steps include: Introducing basic concepts and fundamentals: The first step in teaching music is to introduce students to the basic concepts and fundamentals of music. This includes teaching them about key musical elements such as rhythm, melody, harmony, and form. By providing a solid foundation of knowledge, students can better comprehend the intricacies of music. Demonstrating techniques and skills: To effectively teach music, instructors must demonstrate various techniques and skills to their students. This can involve playing musical instruments, singing, or showcasing different vocal or instrumental techniques. Demonstrations help students visualize and understand the concepts being taught and provide them with a model to emulate. Providing guided practice and feedback: Offering guided practice enables students to apply what they have learned under the instructor’s supervision. Teachers provide specific instructions, corrections, and constructive feedback to help students refine their skills. This step is crucial for the growth and improvement of students’ musical abilities. Facilitating opportunities for independent exploration and creativity: Encouraging students to explore music independently fosters creativity and allows them to develop their own musical style. This can be done through activities such as composition, improvisation, or encouraging students to participate in musical ensembles. Providing opportunities for independent exploration nurtures students’ self-expression and helps them develop a deeper connection with music. Importantly, famous composer Ludwig van Beethoven once said, “To play a wrong note is insignificant; to play without passion is inexcusable.” This quote emphasizes the significance of teaching music with passion and inspires instructors to cultivate a love for music within their students. Furthermore, here are some interesting facts about music education: Research has shown that learning music enhances cognitive skills, including problem-solving, critical thinking, and mathematical abilities. Playing a musical instrument has various benefits on brain development, improving memory, and fine motor skills. Students who engage in music education often demonstrate greater academic achievement and higher standardized test scores compared to their peers. Music education promotes teamwork, discipline, and self-confidence, as students often participate in music groups or performances. Learning music can provide a therapeutic outlet for students, enhancing emotional well-being and reducing stress. In order to present the steps of teaching music in a visually engaging way, here is a simplified table: |Steps of Teaching Music| |1. Introduce concepts and fundamentals| |2. Demonstrate techniques and skills| |3. Provide guided practice and feedback| |4. Facilitate independent exploration and creativity| Remember, teaching music goes beyond the mere transmission of knowledge – it ignites a passion for music, nurtures creativity, and empowers individuals to express themselves through this universal language. In this YouTube video titled “HOW TO TEACH AN ESL SONG – ESL Teaching Tips – with The Singing Walrus,” the speaker discusses the importance of teaching ESL songs and introduces a catchy song called “Rainbow Colors” by The Singing Walrus. They emphasize the need for students to listen to the song first, stopping to explain new words and correct pronunciation. The speaker highlights the importance of singing along with the students and giving them homework to review the song at home. The video also demonstrates a class where the song is taught and reviewed, showing the students’ progress. Additionally, The Singing Walrus emphasizes the benefits of incorporating songs into ESL lessons, as they make learning English enjoyable and improve listening, speaking, and pronunciation skills. They suggest using age-appropriate and topic-relevant songs, as well as gestures, movements, and visual aids to enhance the learning experience. Overall, teaching ESL songs can create a lively and effective learning environment for students. I discovered more solutions online The Orff Approach The least methodical of the four approaches, the Orff method teaches music in four stages: imitation, exploration, improvisation, and composition. There is a natural progression to the method before getting to instruments. 7 Easy Ways to Teach a Primary Song - 1. Teach Song Melody It can be really helpful to start by hearing the music, first thing. - 2. Use Flip Charts or Word Charts - 3. Teach the Song Line-by-Line - 4. Create an Association Teaching the Basics - 1 Warm up with yawning. Before you start practicing singing, have the children take a deep breath and then yawn. - 2 Practice breathing. Children need to learn how to breathe properly when singing. Surely you will be interested in these topics - Establish a Routine for Lesson Planning. This is a stumbling block for many music teachers. - Write It Down. - Consider Standards. - Set a Classroom Routine. - Determine a Sequence. - Choose Themes and Units. - Keep an Ideas List. - Look for New Ideas. - Make The Most Out Of Technology. - Keep The Music You Teach Relevant. - Mix Things Up A Little. - Keep Things Fun. - Inclusivity Is The Key.

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Lesson Plan – Verbs TENER, COMER, ESTAR and HAY to Talk About Food – Food Vocabulary – While reviewing a series of videos, students take note of the food they see and hear. Then, the verbs tener, comer, estar and hay will be presented or reviewed in this context. Finally, they apply what they have learned in this and in previous lessons to improvise a dialogue in pairs of students. – First, students will learn the direct object pronouns’ forms through a video. Then, they create, in pairs, a cheat sheet that they will present to the class —all the students will choose the best, which will be displayed in the classroom. Finally, they carry out three oral activities in order to practice the direct object forms, beginning with those corresponding to yo, tú, then those corresponding to nosotros/nosotras, ustedes and finally the third-person forms, both in singular and plural. During these activities, vocabulary related to food will be used. GOYO Verbs and Lunch Vocabulary – Students will be able to describe the process of making their lunch/ what they bring in their lunches to school using the food vocabulary. By use of oral and written activities, they will be able to demonstrate the use of GOYO irregular verbs and food vocabulary. Negative TU Commands – Cooking Expressions, Food, Appliances, Following a Recipe Lesson Plan – By the end of this lesson, students will be able to use negative commands to express orders to the people and ask questions to confirm whether something should be done or not and understand the answers if negative commands are used. By the end of this activity, students will have reviewed Spanish food vocabulary and learned new Spanish vocabulary to describe the food as well as how to prepare it. Comida tradicional: La identidad pública y privada – Identidad nacional y étnica (México) – In this activity, students learn about Mexican gastronomy, and how food represents the identity of a community.

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Solon was an ancient Greek statesman, lawmaker, and poet who lived in Athens around the 6th century BCE. He is known for initiating a series of reforms that helped to lay the foundation of Athenian democracy. Solon’s life and legacy continue to be celebrated in modern times, as he is considered one of the most important figures in ancient Greek history. Early Life and Career Solon was born into a wealthy family in Athens around 640 BCE. He belonged to the aristocratic class but was also known for his intellectual pursuits. He traveled extensively throughout Greece and beyond, where he gained knowledge about different cultures and political systems. Solon was also a renowned poet, whose works dealt with themes such as justice, morality, and civic responsibility. In 594 BCE, Solon was appointed as archon (magistrate) of Athens during a time of political crisis. The city-state was divided into factions based on social class, with the wealthy landowners and merchants dominating the political scene while the lower classes were marginalized. Solon recognized that this inequality could lead to social unrest and instability. To address these issues, Solon introduced a series of reforms that aimed to create greater equality among citizens. Some of his most significant changes included: - Cancelling all debts and freeing those who had been enslaved due to debt. - Reforming the legal system by abolishing laws that discriminated against certain social classes. - Creating new laws that allowed all citizens to participate in government regardless of their wealth or social status. - Instituting a census that determined each citizen’s wealth level, which determined their eligibility for public office. These reforms helped to create a more just society in Athens, where citizens had more say in how they were governed. Solon’s approach to governance was unique in that he sought to balance the interests of different social classes rather than favoring one over the other. Solon’s reforms had a lasting impact on Athenian society and continue to be studied and celebrated today. His approach to governance helped to pave the way for Athenian democracy, which would develop further over the centuries. In addition, his poetry continues to be an important part of Greek literature, with many of his works still read and studied today. In conclusion, Solon was a visionary leader who recognized the need for greater equality in Athenian society. Through his reforms, he helped to create a more just system of government that allowed all citizens to participate in decision-making. His legacy continues to inspire people around the world who strive for greater democracy and social justice.

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Prepositional phrases KS2 Prepositions are first mentioned in the National Curriculum in Year 3: Writing – vocabulary, grammar and punctuation: use conjunctions, adverbs and prepositions to express time and cause Knowing how to use prepositional phrases allows children to expand their sentences, adding more detail and description. Prepositional phrase activities: - Give children a sticky note and challenge them to write on it as many prepositional phrases as they can find in their current reading book. - Ask children to write a sentence including a prepositional phrase, then swap it with a partner, who has to identify both the preposition and the prepositional phrase. Could they change it for a different prepositional phrase that would still make sense? - Give children a sentence starter, e.g. 'The dog chased the cat...' and ask them to think of how many different prepositional phrases they could add that would complete the sentence. This could be done as a whole class activity - can they each think of a different one? - Give children prepositional phrases as sentence starters, and challenge them to complete the sentence, e.g. 'Beyond the trees...'. You could make this a physical/oral activity by giving children the prepositional phrases on strips of paper, and asking them to travel around the room. When they meet another child, they each have to say aloud a suggestion as to how they would complete the other person's prepositional phrase sentence starter.

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Order of Events Worksheets All About These 15 Worksheets This collection of worksheets will help you understand sequencing, or the order in which events occur in a reading passage. They contain a series of events that are jumbled and must be placed in the correct sequence by the student. They can also have you match images that indicate events in what you have or will read. They are themed on a different variety of topics, including daily life events (like getting ready for school), stories or fairy tales, historical events, scientific processes (like the life cycle of a butterfly), or even math problems that require step-by-step solving. This type of work is a key skill that aids in reading comprehension, narrative writing, understanding historical timelines, scientific processes, and more. Keywords to Look For That Tell Your the Order of Events When reading a passage, there are several types of words and phrases, often referred to as “transitional words” or “temporal words”, that can help you understand the order of events. Knowing and understanding these transitional words and phrases can greatly assist in following the progression of events or ideas within a text. Here are some examples: Sequence Words – These words show the order of events as they happen. - First, second, third, etc. - Before, after - Next, then, afterwards - Finally, lastly Cause and Effect Words – These words show why something happened. - Because, since, therefore, thus - As a result, consequently, hence Comparison and Contrast Words – These words show how things are alike or different. - Similarly, likewise (for comparison) - But, however, on the other hand, whereas (for contrast) Time Words – These words show when events happened. - Now, today, tomorrow, yesterday - Meanwhile, during, while - Soon, later, afterward Additional Information Words – These words add more details or events. - Also, and, furthermore, in addition, moreover. Concluding Words – These words signal that the text or an idea is coming to an end. - In conclusion, to sum up, finally How to Expand On This Skill In The Classroom Teaching the concept of sequence of events can be engaging and interactive. Here are several strategies that you can utilize: Start with Everyday Activities Discuss a common daily routine, such as getting ready for school or baking a cake. Ask students to list the steps in order and discuss the importance of each step occurring at the right time. Teach students common transitional words and phrases that indicate sequence (like first, next, then, finally). Provide exercises for students to practice using these words in their own writing. Picture Books, Short Stories, and Story Maps Picture books and short stories are great tools for teaching sequencing because they often have clear, linear plots. After reading, ask students to retell the story in their own words, focusing on the sequence of events. Create a visual representation of a story’s sequence. This could be a simple linear timeline, a circular “story wheel,” or a more complex flowchart. This helps visual learners see the sequence of events. Sequencing and Writing Prompts Games can make learning fun and engaging. For instance, you could write the sequence of events from a story on individual cards and ask students to arrange the cards in order. Encourage students to write their own short narratives, paying special attention to the sequence of events. This could be a personal narrative or a creative story.

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When it comes to making decisions within a program, developers often face the challenge of choosing the most appropriate conditional statement. Among the popular options are the ‘Switch Case’ and ‘Else-If Ladder’ constructs. These decision-making tools in programming play an important role in controlling the program flow based on certain conditions. However, learning when and how to use each construct optimally can certainly affect code readability, maintainability and performance. What Is An If Ladder Statement? The “else-if ladder,” also known as the “if-else-if-else” chain, is another control flow construct used in programming languages to make multiple conditional checks in sequence. It allows you to evaluate a series of conditions, and if any of them are true, the corresponding code block is executed. If found to be false, it continues to check the next else if ladder statement until the condition comes to be true or the control comes to end the else if ladder statement. The syntax of an else-if ladder is as follows: In an else-if ladder, the program evaluates each condition in order. If a condition is true, the corresponding block of code executes, and the program exits the entire if-else structure. If none of the conditions are true, the code under the else block will be executed. The else-if ladder is useful when you have multiple conditions to evaluate, and the order of evaluation matters. Each condition is checked in sequence, and the first true condition encountered determines the execution path. Features of An else-if-ladder - Zero and non-zero basis is where the else if ladder depends for decision making. - Either integer or character is the variable data type used in the expression of else if ladder. - Each else if has its own expression or condition to be evaluated. - Else if ladder evaluates an expression and then, the code is selected based on the true value of evaluated expression. What Is Switch Case Statement? The “switch case” statement is a control flow mechanism found in many programming languages, including C, C++, Java, and others. It is particularly useful when you have multiple possible values for a single variable and want to execute different blocks of code based on the value of that variable. The syntax of a switch case looks like this: Here, the “variable” is the one whose value you want to check, and the “case” statements represent the possible values it can take. If “variable” matches a particular case, the corresponding code block is executed until it encounters a “break” statement or the end of the switch block. The “default” case is optional and serves as the default code block to execute when none of the specified cases match the value of the variable. Features of Switch Case - The switch case takes decision on the basis of equality. - Each case has a break statement. - Integer is the only data type that can be used in switch expression. - Each switch case will always refer back to the original expression. - The switch statement evaluates the value of an expression and a block code is selected on the basis of that evaluated expression. Which one to use depends on the specific situation. Use a switch case when dealing with a single variable being compared to multiple constant values. On the other hand, use an else-if ladder when dealing with multiple independent conditions, and their order of evaluation is important. What You Need To Know About Switch Case And If-else Ladder - Switch case: It uses the ‘ switch‘ keyword followed by an expression in parentheses. Cases are defined using the casekeyword, and the block of code for each case is enclosed within curly braces. - Else-if ladder: It uses multiple ‘ if‘ statements followed by conditions. The conditions are checked one after the other, and the block of code associated with the first true condition is executed. - Condition evaluation: - Switch case: The expression used in the switch statement is evaluated once, and the control jumps directly to the matching case. This means it is suitable for situations where you need to compare a single value against multiple constants. - Else-if ladder: Each condition in the else-if ladder is evaluated one after the other until a true condition is found. This means all the conditions are checked sequentially, and the control passes through each condition, even if the earlier ones are true. - Supported data types: - Switch case: It can only handle integral data types (e.g., int, char) and certain enumerated types. - Else-if ladder: It can handle any expression that evaluates to a boolean value (true or false). This includes all data types that can be used in boolean expressions. - Expression complexity: - Switch case: The expression inside the switch statement must result in a constant value, meaning it cannot be a complex expression or a range of values. - Else-if ladder: The conditions in the else-if ladder can involve complex expressions, logical operations, and comparisons, allowing for more flexible conditions. - Case matching: - Switch case: The case values must be constant and unique. The control will jump to the first matching case and execute the code within that case. If no match is found, an optional defaultcase can be used. - Else-if ladder: The conditions can be overlapping, meaning multiple conditions can be true for a given input, leading to multiple blocks of code being executed. The order of the conditions matters, and the first true condition is executed. - Fall-through behavior: - Switch case: If a case block does not end with a breakstatement, the control will fall through to the next case and continue executing the code in that case and any subsequent ones until a breakstatement is encountered or the switch block ends. - Else-if ladder: Each ifstatement in the ladder is independent of others, and there is no implicit fall-through behavior like in switch case. - Readability and maintainability: - Switch case: It is more concise and readable when dealing with multiple constant values. It can be a good choice for simple, straightforward scenarios. - Else-if ladder: For complex conditions or ranges of values, an else-if ladder may be more readable and maintainable as it allows expressing conditions more explicitly. - Use cases: - Switch case: It is commonly used when you have a fixed set of values to compare against a single variable and when fall-through behavior is needed (e.g., menu options, handling weekdays). - Else-if ladder: It is used when you have a series of different conditions, each leading to a separate block of code execution, or when you need to evaluate complex expressions. If Else Ladder Vs. Switch Case Statement In Tabular Form |BASIS OF COMPARISON||ELSE IF LADDER||SWITCH CASE| |The control||In else if ladder, the control runs through the every else if statement until it arrives at the true value of the statement or until it comes to the end of the else if ladder.||In else if ladder, the control runs through the every else if statement until it arrives at the true value of the statement or until it comes to the end of the else if ladder.| |Working||Else if ladder statement works on the basis of true false (zero/non-zero) basis.||Switch case statement work on the basis of equality operator.| |Use of Break Statement||In switch, the use of break statement is mandatory and very important.||In else if ladder, the use of break statement is not very essential.| |Variable Data||Integer is the only variable data type that can be in expression of switch.||Either integer or character is the variable data type used in the expression of else if ladder.| |Processing Of Codes||In the case of else if ladder, the code needs to be processed in the order determined by the programmer.||In switch case, it is possible to optimize the switch statement, because of their efficiency. Each case in switch statement does not depend on the previous one.| |Flexibility||Else if statement is not flexible because it does not give room for testing of a single expression against a list of discrete values.||Switch case statement is flexible because it gives room for testing of a single expression against a list of discrete values.| |Usage||Else if ladder is used when there is multiple conditions are to be tested.||Switch case is used when there is only one condition and multiple values of the same are to be tested.| |Values||Values are based on constraint.||Values are based on user choice.|

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In English language, words have various roles to play. Some words may serve as multiple parts of speech depending on their usage in the sentence. This tutorial is going to focus on how the same word can be used as both a preposition and an adverb within a sentence. Understanding Prepositions and Adverbs What are Prepositions? A preposition is a word that shows the relationship between a noun (or a pronoun) and other words in the sentence. It often tells us where or when something is in relation to something else. For instance, in the sentence "The cat is under the table", 'under' is a preposition that shows the relationship between 'the cat' and 'the table'. What are Adverbs? Adverbs are words that modify verbs, adjectives, or other adverbs. Adverbs express manner, time, place, cause, or degree and answer questions such as 'how', 'when', 'where', 'how much'. For example, in the sentence "She ran quickly", 'quickly' is an adverb describing how she ran. When a Word Acts as a Preposition or Adverb There are certain English words that can act as both prepositions and adverbs, depending upon their use in the sentences. Understanding whether a word is being used as a preposition or an adverb often depends on the structure of the sentence and the relationships between the words within it. Word As a Preposition When a word is used as a preposition, it typically connects with a noun or pronoun to create a phrase that modifies another part of the sentence. This phrase provides additional information, such as location, time, or manner. Word As an Adverb When the same word acts as an adverb, it modifies a verb, an adjective, or another adverb. Note that as an adverb, it does not need a noun to complete its meaning. Common Words as Prepositions and Adverbs As a Preposition: 'Around' can mean in a position or direction surrounding, or approximately within a specific area or range. Example: "We walked around the park." As an Adverb: 'Around' can mean existing or in progress, such as in the sentence: "Is there a hotel around?" As a Preposition: 'Before' indicates at an earlier time or previously in location or order. Example: "I arrived before her." As an Adverb: 'Before' indicates at a time preceding the present time. Example: "I have seen that movie before." As a Preposition: 'Down' signifies moving or pointing towards a lower place or position. Example: "He ran down the stairs." As an Adverb: 'Down' means moving from a higher to a lower position, often rapidly. Example: "The bird flew down." Guidelines to Identify the Usage Here are a few general rules to help you identify whether a word is being used as a preposition or an adverb: English language can be tricky, but understanding the roles words can play in sentences is a major step in mastering it. We should remember that prepositions and adverbs, though they can be represented by the same word, play different roles in a sentence structure. Being aware of how a word is being used in a sentence—in context and in relation to the other words—can give us a clear idea of its part of speech.

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In the new National Curriculum (September 2014), there are three Aims central to everything within the Maths content. These are: - Reasoning – following a line of enquiry, conjecturing ideas, and developing an argument, justification or proof using mathematical language; - Fluency – being able to make connections and use what they know to find out what they don’t know, so that pupils develop conceptual understanding; - Problem solving – applying their skills to a variety of problems, breaking them down into smaller steps in order to solve them. Everything we do in Maths is designed to achieve these aims. Every Maths lesson should be a problem solving lesson! Every child is given opportunities to develop their mathematical powers: - Imagine and Express – to picture something inside their head and describe it to others; - Conjecture and convince – to suggest an idea and then try to prove that it is right; - Specialise and generalise – to solve problems individually and also to spot patterns and make general rules; - Organise and classify – to be able to take a collection of data or shapes and sort it out into an order or into groups that are the same. Everybody has mathematical powers! Let’s use them!

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All About These Worksheets This series of Counting Worksheets is designed to develop foundational numeracy skills, enhance number recognition, and foster a love for mathematics. Through a variety of engaging exercises, students will strengthen their ability to count, recognize number patterns, and develop a solid understanding of numerical concepts. From basic counting activities to number sequencing and number identification, these worksheets provide a range of interactive tasks that make learning numbers an enjoyable adventure. This collection also serves as a valuable tool for building numeracy skills, enhancing visual perception, and promoting critical thinking in young learners. Through these worksheets, students will: - Count objects and write the corresponding number, strengthening basic counting skills and number recognition; - Learn to count backwards by filling in the missing numbers, fully grasping the concept of number recognition; - Match the coins to their corresponding names, fostering an appreciation for the practical applications of counting; - And count objects in ten, two, three, four, and five frames and write the corresponding number, promoting subitizing skills and developing number sense. Through this engaging series of Counting worksheets, young learners will develop essential numeracy skills and foster a solid foundation in mathematics. By participating in activities that involve counting objects, subitizing, and number sequencing, students will enhance their ability to recognize and understand numerical concepts. These worksheets provide opportunities for hands-on exploration, critical thinking, and visual perception. By engaging with these exercises, students will develop confidence in their counting abilities, strengthen their number recognition skills, and develop a deeper understanding of the concept of numbers. Ultimately, this collection serves as a stepping stone for a lifelong journey of mathematical discovery and lays the groundwork for future mathematical explorations. How to Teach Kids Counting Skills Teaching kids to count is an essential skill that lays the foundation for more advanced mathematical concepts. Start by teaching your child to count from 1 to 10, using your fingers to demonstrate and encouraging them to follow along. Visual aids, such as flashcards or counting books, can help children associate numbers with their corresponding quantities, promoting number recognition skills. Encourage counting everyday objects, like toys or snacks, to reinforce the concept that numbers represent quantities. Make counting a part of your daily routine, and use songs or rhymes to make it more engaging and enjoyable. Playing simple counting games, such as hide-and-seek or board games that involve counting spaces, can make learning to count more interactive. Teach one-to-one correspondence by touching or pointing to each object as your child counts, and introduce the concept of number order by arranging objects in a sequence. As your child becomes more comfortable with counting, gradually increase the range of numbers they can count to, such as 1 to 20 or 1 to 50. Introduce skip counting (counting by twos, fives, or tens) to help your child develop a sense of number patterns and make counting larger quantities more manageable. Remember that children learn at different paces, so be patient and provide praise and encouragement as your child develops their counting skills. By incorporating counting into everyday activities and using a variety of strategies, you can help your child build strong counting skills that will serve as a foundation for future mathematical concepts. How Often Do We Count? The number of times we count in a day can vary significantly depending on our daily activities, occupation, and personal habits. In general, we tend to count more frequently than we may realize, as counting is often an integral part of many everyday tasks. For example, some common instances where we might count throughout the day include: - Keeping track of time, such as counting minutes or hours. - Counting money, such as when making purchases or counting change. - Measuring ingredients while cooking or baking. - Counting steps while walking or exercising. - Keeping track of repetitions during a workout. - Managing schedules or appointments. - Counting items, such as inventory for work or personal belongings. - Playing games that involve counting, such as card games or board games. These are just a few examples of when we might count during our daily lives. The actual number of times we count in a day will depend on individual circumstances and activities. Some people may count more frequently due to their jobs, such as accountants, statisticians, or retail workers, while others may count less frequently. Nonetheless, counting remains an essential skill for navigating various aspects of everyday life.

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Mechanical Waves: These travel through a material medium. Electromagnetic Waves: EM waves do not require a material medium to exist. Matter or Quantum Mechanical Waves: These describe the motion of elemental particles (electrons, protons, etc.) on the atomic level. We won't investigate them in this course. We also classify waves based on how they move: Transverse Waves: The particles of the wave move perpendicular to the motion of the wave. Longitudinal Waves: The particles of the wave move parallel to the motion of the wave. This is done through compression and rarefaction (expansion), i.e., the wave is transmitted by pressure changes. We describe a wave with the following characteristics: Amplitude (A): How tall the wave is at its maximum height. Wavelength (λ): The distance between "repeating" points on the wave, such as top-to-top. Wave speed (v): How fast the wave is moving. Period (T): The time it takes to go through a full oscillation. Frequency (f): The number of oscillations that occur per second. [The unit for this is the hertz (Hz) where 1 Hz = [1/1s]. Thus, f = [1/T] and T = [1/f].] Because speed, frequency, and wavelength are all related, v = λf . We can find the height (or pressure differential if it's a longitudinal wave) with the following equation: y(x,t) = Asin(kx − ωt). x is the horizontal location we are considering. t is the time we are looking at the wave. k is the angular wave number and is connected to the wavelength: ω is the angular frequency and is connected to the period (which is connected to the frequency): ⇔ ω = 2π·f. Intro to Waves Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture. This book includes a set of features such as Analyzing-Multiple-Concept Problems, Check Your Understanding, Concepts & Calculations, and Concepts at a Glance. This helps the reader to first identify the physics concepts, then associate the appropriate mathematical equations, and finally to work out an algebraic solution.

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5 Written Questions 5 Matching Questions - Centrifugal ("Center-Fleeing") Force - Stick about end: - Center of mass (CM) - axis (pl. axes) - center of mass - a Point at the center of an objects mass distribution, where all its mass can be considered to be concentrated. For everday conditions, it is the same as the center of gravity. - b I = 1/3 mL² - c (a) Straight line about which rotation takes place. (b) Straight lines for reference in a graph, usually the x-axis for measuring horizontal displacement and the y-axis for measuring vertical displacement. - d This force is not an actual force; it is a fictitious force that seems to pull outwards on an object on a circular path. This effect is due to inertia, or the tendency for a moving object to follow a straight path. - e The average position of the mass of an object. The CM moves as if all the external forces acted at this point. 5 Multiple Choice Questions - L = Iω where L (angular momentum) translates to linear momentum (p), and I (moment of inertia) translates to mass (m), and ω (angular velocity) translates to velocity (v). This is the translation from rotational (circular world) terms to linear terms (linear world). - the tendency of a force to rotate an object about an axis (force x lever arm) - the straight line around which rotation occurs - the amount of time it takes to complete one cycle (1 revolution) - In the absence of a net external force, the momentum of an object or system of objects is unchanged. 5 True/False Questions rotational inertia → Number of rotations or revolutions per unit of time. Equilibrium → In general, a state of balance. For mechanical equilibrium, the state in which no net forces and no net torques act. Rotational Inertia → Number of rotations or revolutions per unit of time. machine → the straight line around which rotation occurs Pendulum → Inertia in motion. The product of the mass & velocity of an object (provided the speed is much less than the speed of light) has magnitude & direction & therefore is a vector quantity. Also called linear momentum & abbrieviated p=mv

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Presentation on theme: "Some material in this presentation is used under the fair use exemption of US copyright law. Further use is prohibited."— Presentation transcript: Some material in this presentation is used under the fair use exemption of US copyright law. Further use is prohibited. A Science Fair Project has 5 steps. 1.Find an idea 2.Research and Hypothesis 3.Designing your Experiment 4.Data and Conclusion 5.Putting it all Together The Scientific Method 1.Ask a question. Who? What? Where? When? Why? How? Which? The Scientific Method 2. Research the Question. This gives you information about your question. The Scientific Method 3.Form a hypothesis. A hypothesis is an educated guess about the answer to your question. The Scientific Method 4. Do an experiment to test your hypothesis. The Scientific Method 5. Analyze your data and draw a conclusion. What did your experiment prove? The Scientific Method 6. Present your Results. Tell the world what you know. The Library has a bunch of Science Fair project idea books. Places to Look for an Idea Discovery Channel Exploratorium Fact Monster How Stuff Works: Science NASA How to Cite a Source Book last name, first name. Title. Place: publisher, date. Magazines Author. “Title.” Magazine. Date:page. How to Cite a Source Database Author. “Title.” Magazine. Date: page. Name of the Database. Date of Access. Web address. Website Title of Site. Editor. Date. Name of Sponsoring Institution. Date of Access.. How to Cite a Source Or create an account on: Bibme Works Cited Haduch, Bill. Science Fair Success Secrets. New York: Dutton Children’s Books, Hirschmann, Kris. You Can Create a Killer Science Fair Project. New York: Scholastic, 2010.

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W = F * CosΘ * s The work performed is composed of two vectors, which are: Force (F) and Displacement (s). This means that work is the scalar productof these two vectors. Since we consider the direction too, besides the magnitude, in a vector, we have to take into account that for these two vectors (force and displacement) there is also adirection, which it is going to be represented in the formula as the angle (Θ) that is formed between them. Since we know that work only depends on its starting and ending position, we have as a fact thatwork is a scalar quantity, which means that the direction is not relevant, work does not have an ascertained direction, even though it is formed by two vectors. From all the above information, wefinally gathered that to have work, we must have two important elements. There must exist force acting on the object, and there must exist a displacement of the final position of the object. It is veryimportant that both elements are present to perform work, if one of them is missing, no work will be performed. When performing an operation regarding work, on this chapter, you are going to see adrawing like this: Y N Fy F fk Θ X The picture shows forces being applied to an object on a horizontal surface, thedisplacement (s) is not shown in the picture, but usually the magnitude will be given on the problem. We can notice that there is a force (F) applied to the object at a certain angle (Θ), which opens force ony-axis (Fy) and force on x-axis (Fx). We also see kinetic friction (fk), Normal force (N), and Weight (W). Now, we’re going to show some examples that will help to have a better understanding aboutthe performing of work and the importance of its elements (force and displacement): * If there is no displacement on the object, no work will be done. S = 0, then W = 0 If you are pushing...

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Did you know that even wordless books (picture books with no words) can foster important literacy skills? They can: - Develop oral language and sequencing skills as a child “reads” using imagination and prediction. - Prompt discussion of storyline and story structure (“What happened at the beginning of the story? The middle? The end? Why?) - Lead to literacy-rich conversations full of vocabulary words far above a child’s reading level and make connections to a child’s life experience. (Did you ever see a rhinoceros at the zoo?”) - Foster higher-level thinking: (“Can you think of animals other than birds that can fly?” “Why can’t pigs fly in real life?”) - Teach book handling and conventions: how to hold a book right side up, how to turn pages, and that we read from left to right. So try incorporating wordless books into your story times and see what happens. The imaginations of the children in your life may just leave you speechless.

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Squaring with Squares One of the proofs of the Pythagorean Theorem typically uses squares constructed on each side of a right triangle (see figure below). The area of the square constructed on the hypotenuse (green square) is equal to the sum of the areas of the squares constructed on each of the legs of the triangle (blue squares). View a dynamic version of this construction in Geometer's Sketchpad or in a java template. Instead of using squares, can we use equilateral triangles? How about regular hexagons? Would these figures (or any others) give the same results? What is so special about squares? In other words, why are squares typically used in this proof? || Related External Resources Heron's Area of a Triangle This site will take you through some historical explorations, some interactive activities, and some intriguing connections in mathematics. Geoboards in the Classroom This unit deals with the side lengths and area of two-dimensional geometric figures using the geoboard as a pedagogical device. Dissecting the Pythagorean Theorem This lesson is for students to develop an understanding of how and why the Pythagorean theorem works. Also, students will gain an understanding of applications of the theorem and relate it to real world situations. Submit your idea for an investigation to InterMath.

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Chapter 4 Practice Problems # 11, 14, and 18 11. List the five steps of hypothesis testing, and explain the procedure and logic of each. 1. Restate the question as a research hypothesis and a null hypothesis about the populations. It is useful to restate the research question in terms of populations. 2. Determine the characteristics of the comparison distribution. The overall logic of hypothesis testing involves figuring out the probability of getting a particular result if the null hypothesis is true. So, you need to know what the situation would be if the null hypothesis were true. The comparison distribution is the distribution that represents the population situation if the null hypothesis is true. 3. Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected. Before conducting a study, researchers set a target against which they will compare their result: how extreme a sample score they would need to decide against the null hypothesis, that is, how extreme the sample score would have to be for it to be too unlikely that they could get such an extreme score if the null hypothesis were true. This is called the cutoff sample score. 4. Determine your sample’s score on the comparison distribution. This step is to get the actual results for the sample. Once you have the results for your sample you figure the Z score for the sample’s raw score. 5. Decide whether to reject the null hypothesis. Compare the sample’s Z score to the cutoff Z score and decide whether to reject the null hypothesis. 14. Study Sample Score p Tails of Test A 5 1 7 .05 1 (high predicted) B 5 1 7 .05 2 C 5 1 7 .01 1 (high predicted) D 5 1 7 .01 2... Please join StudyMode to read the full document

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1. (100 pts) Write a program to construct a binary search tree and print the tree on its side. Read the input from the user as a sequence of integers and output the tree indented based on depth and with one value on each line. Consider the following input from user Enter the numbers 10 6 14 4 8 12 16 The binary search tree using above numbers is given below Figure 1: Binary Search Tree Note that the order of the numbers entered changes the tree. First number is always the root of the tree and last number is a leaf of the tree. The output for the above set of numbers is the tree printed on its side as shown below. The text for a node should be indented 4 times the depth of the node. Root (depth 0) should not be indented and a node at depth 2 should be indented 8 spaces.

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Problem-Solving Decisions: Choose a Method Practice In this math methods worksheet, students solve the decimal word problems and then write which computation method they used to solve with. 3 Views 0 Downloads - Activities & Projects - Graphics & Images - Lab Resources - Learning Games - Lesson Plans - Primary Sources - Printables & Templates - Professional Documents - Study Guides - Writing Prompts - AP Test Preps - Lesson Planet Articles - Interactive Whiteboards - All Resource Types - Show All See similar resources: Unit Conversions and Problem Solving with Metric Measurement Convert young mathematicians' knowledge of place value into an understanding of the metric system with this five-lesson unit. Through a series of problem solving activities and practice exercises, students learn about the relationship... 3rd - 5th Math CCSS: Designed Fraction and Decimal Word Problems No Problem! Searching for a way to improve young mathematicians' problem solving skills? Look no further. This comprehensive collection of word problem worksheets has exactly what you need to help students apply their understanding of fractions,... 4th - 7th Math CCSS: Adaptable Deciphering Word Problems in Order to Write Equations Help young mathematicians crack the code of word problems with this three-lesson series on problem solving. Walking students step-by-step through the process of identifying key information, creating algebraic equations, and finally... 5th - 8th Math CCSS: Adaptable Problem Solving Strategy: Solve a Simpler Problem - Reteach 6.6 In this problem solving strategies worksheet, students solve 2 word problems where they use models and the "solve a simpler problem strategy" to help them solve the problem. The problems contain fractions. A detailed example that uses a... 5th - 8th Math Solve Addition Problems: Using Key Vocabulary Being able to identify key words can make all the difference when solving word problems. The first video in this series on problem solving models how to locate specific words that indicate the solution to a question that involves... 4 mins 2nd - 4th Math CCSS: Designed Solve Word Problems Involving Multiplying a Fraction by a Whole Number Learning math provides people with the necessary skills for dealing with life's everyday problems. The second video in this two-part series teaches young mathematicians how to apply their skills with multiplying fractions by whole... 4 mins 3rd - 5th Math CCSS: Designed Solve Real World Problems by Finding the Area of a Rectangle Young mathematicians learn to apply their understanding of area in real-world contexts with the final video of this series. Multiple examples are presented that demonstrate different situations that involve calculating the area of a... 8 mins 2nd - 4th Math CCSS: Designed

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Although its interior is invisible, a black hole may reveal its presence through an interaction with matter that lies in orbit around it. A black hole can be perceived by tracking the movement of a group of stars that orbit its center. One may observe gas from a nearby star that has been drawn into the black hole. The gas spirals inward, heating up to very high temperatures and emitting large amounts of radiation that can be detected from earthbound and earth-orbiting telescopes. A black hole is the evolutionary endpoint of star at least 10 to 15 times as massive as the Sun. If a star that massive undergoes a supernova explosion, it will leave behind a fairly massive burned out stellar remnant. With no outward forces to oppose gravitational forces, the remnant will collapse in on itself, that is to say it will implode, collapsing to the point of zero volume and infinite density, thus creating what is known as a singularity. As the density increases, the path of light rays emitted from the star are bent and eventually wrapped irrevocably around the star. Any emitted photons are trapped, too, by the intense gravitational field. Because no light escapes after the star reaches this infinite density, it is called a black hole. Supermassive black holes that contain hundreds of thousands to billions of solar masses are believed to exist in the center of most galaxies, including our own Milky Way. They are thought to be responsible for active galactic nuclei, and form either from the coalescence of smaller black holes, or by the accretion of stars and gas onto them. The largest known supermassive black hole is located in OJ 287 weighing in at 18 billion solar masses.

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If you are teaching your child how to write the alphabet, interact with them as they write each letter. Once they finish writing the letter a and the letter b, for example, ask them about the differences between each letter. This will help your child remember each letter and start to get a sense of the different shapes of each letter. 1 2, make the letter. Draw one angled vertical line facing right: /. Draw another angled vertical line facing left:, ensuring both lines touch each other at the top upper tips: /. Alphabet Letters, worksheets beker, henry; Piper, Fred (1982). Cipher Systems: The Protection of Communications. Table also available from Lewand, robert (2000). Mathematical Association of America. Archived from the original. Retrieved Further reading edit michael Rosen (2015). Alphabetical: How every letter Tells a story. Uppercase letters, these exercises support letter recognition through reading and writing uppercase letters. We confine each letter to one page so your child can clearly see how letter forms differ from one another. W and y are sometimes referred as semivowels by linguists. See also edit see also the section on Ligatures often in Hiberno-English, due to the letter's pronunciation in the Irish language mostly in Hiberno-English, sometimes in Australian English, usually in Indian English citation needed (although often considered incorrect) citation needed, and also used in Malaysian. The spelling qu que is obsolete, being attested from the 16th century. in Hiberno-English in compounds such as es-hook write especially in American English, the /l/ is often not pronounced in informal speech. (Merriam Webster's Collegiate dictionary, 10th ed). Common colloquial pronunciations are /dʌbəju/, /dʌbəjə/, and /dʌbjə/ (as in the nickname "Dubya especially in terms like www. in British English, hiberno-English and Commonwealth English in American English References edit "Digraphs (Phonics on the web. a b Michael everson, evertype, baldur Sigurðsson, Íslensk málstöð, On the Status of the latin Letter Þorn and of its Sorting Order "m definition". Retrieved 18 September 2016. In English and many other languages it is used to represent the word and and occasionally the latin word et, as in the abbreviation c (et cetera). Apostrophe edit The apostrophe, while not considered part of the English alphabet, is used to contract English words. A few pairs of words, such as its (belonging to it ) and it's ( it is or it has were (form of 'to be and we're (we are and shed (to get rid of) and she'd ( she would or she had ) are. The apostrophe also distinguishes the possessive endings -'s and -s' from the common plural ending -s, a practice introduced in the 18th century; before, all three endings were written -s, which could lead to confusion (as in, the Apostles words ). 5 Phonology edit main article: English phonology The letters a, e, i, o, and u are considered vowel letters, since (except when silent) they represent vowels ; the remaining letters are considered consonant letters, since when not silent they generally represent consonants. However, y commonly represents vowels as well as a consonant (e.g., "myth as very rarely does W (e.g., " cwm. Conversely, u and I sometimes represent a consonant (e.g., "quiz" and "onion" respectively). Alphabet, worksheets, writing the, alphabet, worksheets (see latin alphabet: Origins.) The regular phonological developments (in rough chronological order) are: palatalization before front vowels of Latin /k/ successively to /tʃ /ts and finally to middle French /s/. Palatalization help before front vowels of Latin /ɡ/ to Proto-romance and Middle French /dʒ/. Fronting of Latin /u/ to middle French /y becoming Middle English /iw/ and then Modern English /ju/. The inconsistent lowering of Middle English /ɛr/ to /ar/. The Great Vowel Shift, shifting all Middle English long vowels. Affects a, b, c, d, e, g, h, i, k, o, p, t, and presumably. The novel forms are aitch, a regular development of Medieval Latin acca ; jay, a new letter presumably vocalized like neighboring kay to avoid confusion with established gee (the other name, jy, was taken from French vee, a new letter named by analogy with the. Some groups of letters, such as pee and bee, or em and en, annual are easily confused in speech, especially when heard over the telephone or a radio communications link. Spelling alphabets such as the icao spelling alphabet, used by aircraft pilots, police and others, are designed to eliminate this potential confusion by giving each letter a name that sounds quite different from any other. Frequencies edit main article: Letter frequency The letter most commonly used in English. The least used letter. The frequencies shown in the table may differ in practice according to the type of text. 4 Ampersand edit The has sometimes appeared at the end of the English alphabet, as in Byrhtferð's list of letters in 1011. 2 Historically, the figure is a ligature for the letters. derived forms (for example exed out, effing, to eff and blind, etc. and in the names of objects named after letters (for example em (space) in printing and wye (junction) in railroading). The forms listed below are from the Oxford English Dictionary. Vowels stand for themselves, and consonants usually have the form consonant ee or e consonant (e.g. Bee and ef ). The exceptions are the letters aitch, jay, kay, cue, ar, ess (but es- in compounds double u, wye, and zed. Plurals of consonants end in -s ( bees, efs, ems ) or, in the cases of aitch, ess, and ex, in -es ( aitches, esses, exes ). Plurals of vowels end in -es ( aes, ees, ies, oes, ues these are rare. All letters may stand for themselves, generally in capitalized form ( okay or ok, emcee or mc and plurals may be based on these ( aes or As, cees or Cs, etc. ) Letter Name name pronunciation Frequency modern English Latin Modern English Latin Old French Middle English a a ā /eɪ/, /æ/ nb 2 /a/ /a/ /a/.17 B bee bē /bi/ /be/ /be/ /be/.49 C cee cē /si/ /ke/ /tʃe/ /tse/ /se/ /se/.78. Ju/ nb.36 x ex ex /ɛks/ /ɛks/ /iks/ /ɛks/.15 ix /ɪks/ Y wy hȳ /waɪ/ /hy/ ui, gui? 1.97 /i/ ī graeca /i ɡraɪka/ /i ɡrɛk/ z zed nb 9 zēta /zɛd/ /zeta/ /zɛdə/ /zɛd/.07 zee nb 10 /zi/ Etymology edit The names of the letters are for the most part direct descendants, via french, of the latin (and Etruscan) names. University, statement of, purpose, editors, writing Diacritics are also more likely to be retained where there would otherwise be confusion with another word (for example, résumé (or resumé ) rather than resume table and, rarely, even added (as in maté, from Spanish yerba mate, but following the pattern of café, from French). Occasionally, especially in older writing, diacritics are used to indicate the syllables of a word: cursed (verb) is pronounced with one syllable, while cursèd ( adjective ) is pronounced with two. È is used widely in poetry,. Tolkien uses ë, as in O wingëd crown. Similarly, while in chicken coop the letters -oo- represent a single vowel sound (a digraph in obsolete spellings such as zoölogist and coöperation, they represent two. This use of the diaeresis is rarely seen, but persists into the 2000s in some publications, such as mit technology review and The new Yorker. An acute, grave, or diaeresis may also be placed over an "e" at and the end of a word to indicate that it is not silent, as in saké. In general, these devices are often not used even where they would serve to alleviate some degree of confusion. Letters edit The names of the letters are rarely spelled out, except when used in derivations or compound words (for example tee-shirt, deejay, emcee, okay, aitchless, etc. Some bloody fonts for typesetting English contain commonly used ligatures, such as for tt, fi, fl, ffi, and ffl. These are not independent letters, but rather allographs. Proposed reforms edit Alternative scripts have been proposed for written English mostly extending or replacing the basic English alphabet such as the deseret alphabet, the Shavian alphabet, gregg shorthand, etc. Diacritics edit main article: English terms with diacritical marks diacritic marks mainly appear in loanwords such as naïve and façade. As such words become naturalised in English, there is a tendency to drop the diacritics, as has happened with old borrowings such as hôtel, from French. Informal English writing tends to omit diacritics because of their absence from the keyboard, while professional copywriters and typesetters tend to include them. 3 Words that are still perceived as foreign tend to retain them; for example, the only spelling of soupçon found in English dictionaries (the oed and others) uses the diacritic. were both replaced by th, though thorn continued in existence for some time, its lowercase form gradually becoming graphically indistinguishable from the minuscule y in most handwriting. Y for th can still be seen in pseudo-archaisms such as "ye olde booke shoppe". The letters þ and ð are still used in present-day icelandic while ð is still used in present-day faroese. Wynn disappeared from English around the 14th century when it was supplanted by uu, which ultimately developed into the modern. Yogh disappeared around the 15th century and was typically replaced. The letters u and j, as distinct from v and i, were introduced in the 16th century, and w assumed the status of an independent letter, so that the English alphabet is now considered to consist of the following 26 letters: he variant lowercase form. Ligatures in recent usage edit outside of professional papers on specific subjects that traditionally use ligatures in loanwords, ligatures are seldom used in modern English. The ligatures æ and œ were until the 19th century (slightly later in American English) citation needed used in formal writing for certain words of Greek or Latin origin, such as encyclopædia and cœlom, although such ligatures were not used in either classical Latin. These are now usually rendered as "ae" and "oe" in all types of writing, citation needed although in American English, a lone e has mostly supplanted both (for example, encyclopedia for encyclopaedia, and maneuver for manoeuvre ). Futhorc influenced the emerging English alphabet by providing it with the letters thorn (Þ þ) and wynn ( ). The letter eth (Ð ð) was later devised as a modification of dee (D d and finally yogh ( ) was created by norman scribes from the insular g in Old English and Irish, and used alongside their Carolingian. The a-e ligature ash (Æ æ) was adopted as a letter in its own right, named after a futhorc rune æsc. In very early Old English the o-e ligature ethel (Œ œ) also appeared as a distinct letter, likewise named after a rune, œðel citation needed. Additionally, the v-v or u-u ligature double-u essay (W w) was in use. In the year 1011, a monk named Byrhtferð recorded the traditional order of the Old English alphabet. 2 he listed the 24 letters of the latin alphabet first (including ampersand then 5 additional English letters, starting with the tironian note ond an insular symbol for and : y z þ ð æ modern English edit In the orthography of Modern English, thorn. Kite runner Title: meaning significance The modern, english alphabet is a, latin alphabet consisting of 26 letters, each having an uppercase and a lowercase global form: The same letters constitute the, iso basic Latin alphabet. The exact shape of printed letters varies depending on the typeface (and font ). The shape of handwritten letters can differ significantly from the standard printed form (and between individuals especially when written in cursive style. Written English has a number 1 of digraphs, but they are not considered separate letters of the alphabet: ch ci ck gh ng ph qu rh sc sh th ti wh. also use two ligatures, æ and œ, nb 1 or consider the ampersand ( ) part of the alphabet. Contents History edit see also: History of the latin alphabet and English orthography Old English edit main article: Old English Latin alphabet The English language was first written in the Anglo-saxon futhorc runic alphabet, in use from the 5th century. This alphabet was brought to what is now England, along with the proto-form of the language itself, by Anglo-saxon settlers. Very few examples of this form of written Old English have survived, these being mostly short inscriptions or fragments. The latin script, introduced by Christian missionaries, began to replace the Anglo-saxon futhorc from about the 7th century, although the two continued in parallel for some time.

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This free e-book is a WRITING ACTIVITY about The Polar Express. Students will imagine that they are the little boy in The Polar Express story. Then, students will write their responses accordingly. Read The Polar Express. Have a discussion about the story. -Who are the characters in the story? -What happened in the beginning, middle and end of the story? -Answer the 5W's. Who?, Did what?, Where?, When? and Why? -Identify the problem and the solution for several events in the story. *Introduce this writing activity. -Make sure to model how this activity should be completed. Especially for the beginning writers. *General directions are given on the front cover of the book. Teacher should give complete instructions and expectations for this activity. *You will see that I included the basic directions on the front cover of the book. -Beginning Writers will: 1)Read each sentence prompt. (beginning readers will need teacher assistance) 2) Illustrate your response (with as much detail as possible) 3) Write 1- 2 sentences. (this can be modified for -Advanced Writers will 1) Read each sentence prompt. 2) Illustrate their response. 3)Write their response. (Teacher will decide how many sentences are expected.) 4)Add detail. 5) Use descriptive words. Please follow my store for updates, Lidia R. Barbosa -Please follow my blogs and facebook pages for even more updates and ideas: 1. Kinder Alphabet blog

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A Sample of Second Grade English Language Arts and Literacy Common Core State Standards ■ Paying close attention to details, including illustrations and graphics, in stories and books to answer who, what, where, when, why, and how questions ■ Determining the lesson or moral of stories, fables, and folktales ■ Using text features (e.g., captions, bold print, indexes) to locate key facts or information efficiently ■ Writing an opinion about a book he or she has read, using important details from the materials to support that opinion ■ Writing stories that include a short sequence of events and include a clear beginning, middle, and end ■ Taking part in conversations by linking his or her comments to the remarks of others and asking and answering questions to gather additional information or deepen understanding of the topic ■ Retelling key information or ideas from media or books read aloud ■ Producing, expanding, and rearranging sentences (e.g., “The boy watched the movie”; “The little boy watched the movie”; “The action movie was watched by the little boy”) ■ Determining the meaning of the new word formed when a known prefix or suffix is added to a known word (happy/unhappy; pain/painful/painless) There are a variety of reading strategies that students use when they read. "Sounding out" is often used as the only method to read a word, but there are other strategies that are taught. Students should be thinking about not just stretching out sounds, but also about what makes sense in the sentence. Refer to the image below for a list of reading strategies that are reinforced in second grade. As students in second grade are working on using a variety of reading strategies, the emphasis on fluency becomes a priority. Fluency is the ability to read smoothly. It can also involve reading with expression. The reason we reinforce fluency is because research has shown that most students who are not fluent often have issues with comprehension. If it takes a student longer to read, it often makes it harder to remember what was actually read. One of the main prompts teachers use with students who are not fluent, is to encourage students to "put your words together like you are talking." If your child is having issues with phonics, refer to the web resources below to help strengthen those skills. As students begin to read longer texts, it's important to ask them questions to be sure that they understand what they are reading. It's not only important to ask questions when students are reading the books themselves, but also when a book is being read to them. Second grade teachers at Pocasset have been using the CAFE reading strategies that have been developed by Gail Boushey and Joan Moser to address students' comprehension, accuracy, fluency, and vocabulary. The image below explains these strategies in more detail. Sight words are words students should be able to recognize quickly by sight. Many of them are "rule breakers" and don't follow a regular pattern for sounding out purposes. Students practice reading and writing these words all throughout second grade. Refer to the link below for the 100 words that are taught in second grade. The link also includes ready to print flashcards. Most students read between a Level I and M or above in second grade. Once you know your child's reading level, you can refer to the links below to print, purchase and/or borrow books at your child's level. Below you will find some interactive sites that will be helpful in reinforcing second grade reading skills.

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If speed has an effect on the impact of collisions, what happens if an object changes speed? - Do Now– Get out your Acceleration Lab worksheet. Write your name on your paper and answer the question: What are three ways an object can accelerate? - Science Friday– The Bouba-Kiki Effect - Video Segment– Science of NFL Football: Position, Velocity, & Acceleration - Investigation– Acceleration- Observe what happens with the accelerometer. What pieces of the puzzle did we figure out? Review answers to lab questions. - Driving Question Summary Table– Complete the DQST on ISN pgs. 50-51 for the Acceleration lab. How do different factors affect an object’s speed? How does an object’s speed affect its impact? - Do Now– Copy down your Home Learning task in your planner. Get out your science notebook and open to page 55. Read your definition of a reference point. Write your name on your paper and answer: What reference point would you have to use to be moving right now while you sit in your seat? - Investigation– Calculating Speed and Determining Velocity- Observe a collision into a barrier on the demonstration track. Finish graphing your data. Answer all of the lab questions, including Reflect and Apply. What pieces of the puzzle did we figure out? - Driving Question Summary Table– Complete the DQST on ISN pgs. 50-51 for the Calculating Speed and Determining Velocity lab. Complete the questions on the Calculating Speed Lab What happens when objects collide? - Do Now– Copy down your Home Learning assignment in your planner. Get out your science notebook and add to the Table of Contents- “DQST p.50″ (Left Side), “DQST p.51” (Right Side), “DQST p.52” (Left Side), and “DQST p.53” (Right Side). - Class Consensus Initial Model– Together, let’s look at samples of models in Google Slides so we can see if our explanations agree and in what areas we disagree. From that discussion, we will build a Class Consensus Initial Model. Tape your model as a flip page to ISN p.48. - Develop Questions/Driving Question Board– What do we need to figure out to explain all of this? Brainstorm “What We Wonder” questions about colliding objects and make a list of those questions on ISN p.48. For each of your observations on ISN p.49, think about a question that you can investigate to help you better understand it. Choose the most compelling or interesting question from ISN p.48 and write it big and bold on a notecard using a marker. Write your initials and period number in pencil on the front corner of the card. Bring your card to the scientists’ circle. Read your question and post it on the Driving Question Board (DQB). Explain how it is related to another question on the board. - Driving Question Summary Table (DQST)– Set up the DQST on ISN pages 50-53 for the driving question: How can we design a crash protection device to absorb enough energy during a car crash to save lives? Ideas for Investigation/Next Steps– Which of the questions from ISN p.48 or from the Driving Question Board (DQB) would you like to investigate further? What would you like to do to investigate any of those questions? (See Question in Classwork in Google Classroom under Today topic.) Do liquids follow the same rules for sinking and floating as solids? Do all liquids have the same density as water? - Do Now– Copy down your homework assignment in your planner. Get out your science notebook to pages 52-53. - Driving Question Summary Table– Complete the DQST on ISN pgs. 52-53 for the Sinking and Floating Investigations on ISN pgs. 62-65. - Final Model/Explanation- Watch the phenomenon again carefully. Also check out this person floating in the Dead Sea, these large floating ducks, and floating lemons but sinking limes. What determines whether something sinks or floats? On the white paper, draw your ideas of what you have learned is happening when something sinks or floats. - Practice– Take It Further Questions 7-10 handout Science Notebooks (ISN’s) due as follows: - Monday 4/30- Period 3 - Tuesday 5/1- Period 4 - Wednesday 5/2- Period 2 - Thursday 5/3- Period 6 - Friday 5/4- Period 7 What is the density of water? Do different amounts of matter (like water) have the same density? - Do Now- Copy down your homework assignment in your planner. Get out your science notebook and open to pages 52-53. Work on your Voice Finder. Find and answer question 1, then follow the dashed line to each question to think about and answer each one. - Driving Question Summary Table– Complete the DQST on pages 52-53 for the Density of Water Investigation on ISN pgs. 60-61. - Formative Assessment– Density of Water Complete Take It Further (Question 9) handout

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In this problem students explore shapes and investigate how large a closed container they can make. They should be encouraged to construct shapes other than cubical boxes. Some may need to be reminded of the formula for the particular volume that they make. Tipene and his friends have scissors, tape and sheets of A4 paper to construct closed containers from a single sheet of paper. Tipene's net is a single piece that can be folded or bent to make the container. (He joins the sides with tape not tabs.) Miri makes a shape where the net is not one piece but can be taped together to make the container (making a more efficient use of paper). Pepe makes a shape where one face is a square. Who makes the container with the biggest volume? - Begin by giving the students a piece of A4 paper and ask them to make a closed container. At this stage keep the requirements open. - Display the containers and discuss: Which is the largest? What criteria have you used in making your decision? Which container has the largest surface area? How do yo know? Which container has the smallest surface area? Which container has the largest volume? Do any of the containers have square faces? - Pose the problem to the class. - Ask for their initial ideas about which container has the greatest volume. Ask them to explain the thinking behind their guess. - Take votes for the containers. List results on the board. - Have the students investigate the problem in pairs - As the students work ask questions that focus on their understanding of area, volume and perimeter. What is the area of this faces? How did you work it out? What is the volume of your container? How did you work it out? What sort of container do you think will have the largest volume? Why? How did you start on this problem? What understandings are you using to solve this problem? - When the students think that they have a solution for the largest container, ask them to make the container from a single sheet of A4. Share and discuss containers. Ask: Do you think we have found the container with the largest volume? How do we know? There is no one solution to this problem. The idea here is to explore shapes and to find ways to measure their volume.

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Tabla para escribir los números en español basada en los valores de posición. Place Value based chart to write numbers in Spanish. Log in to see state-specific standards (only available in the US). Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: 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.

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This chapter discusses the different English adverbs. These different adverbs differ in their meaning and usage. The different adverbs are described in the subchapters. Adverbs are used to explain in what way someone does something. Adverbs add information about the word they are connected to. The adverbs are able to modify verbs, adjectives, clauses, sentences and other adverbs. Adverbs are formed by: adjective + ly Adverbs are used to give more information about other words, usually verbs. Giving us more information about how often, when, or where an action took place. |Modify other adverbs|| The adjectives are turned into an adverb when adding '-ly'. Rule: adjective + ly Keep in mind: |Adjective ends in '-y'|| |Adjective ends in '-able', '-ible', '-le'|| |Adjective ends in '-ic'|| Most adverbs are formed by adding '-ly' to an adjective. However, there are some exceptions, which are shown in the table below. |wrong||wrong, or wrongly| The table below shows the different types of adverbs. |Adverb||Position in the sentence||Example| |Place||Placed at the end of the sentence.||The child played outside.| |Manner||Placed after the verb.||He sings well.| |Degree||Placed before the adjective or adverb.||The presentation was quite interesting.| |Frequency||Placed before the verb, but after the verb 'to be'.||He is always on time.| |Time||Placed at the end of the sentence and after place.||She was late today.| |Certainty and probability||Placed depending on the sentence.||He will definitely come tonight.| |Opinion and observation||Placed at the beginning of the sentence.||Obviously, she will come to the party tonight.| |Quantity||Placed before the adjective or adverb.||There are many students absent today.| When there are multiple adverbs in a sentence, there is an order for the adverbs: The other adverbs will be placed depending on the nouns in the sentence or the type of sentence that is formulated. Train your skills by doing the exercises! |1 Position of adverbs in English| |2 Adverbs of manner in English| |3 Adverbs of place in English| |4 Adverbs of time in English| |5 Adverbs of quantity in English| |6 Adverbs of frequency in English| |7 Adverbs of degree in English| |8 Adverbs of probability and certainty in English| |9 Adverbs of opinion and observation in English| 4.1/5 from 3 reviews Hi, First of all, I would like to congratulate you on the decision to learn or improve a new language. Whether it is Estonian, English or... Russian, beginner, advanced or Business language - you are in the right place. My name is Martin and I am coming from a tiny country in the Northern Europe called Estonia. One of my biggest hobbies is teaching and educating others, that is why for the past 3 years I have been living and working in Istanbul while teaching English to different age groups: kindergarten, school, university as well as adults. I have had students from Beginners to Advanced as well as several businessmen and CEOs of international companies located in Istanbul. What is more, for the last 2 years I have been teaching Estonian, English and Russian online through Skype that gave me chance to meet people from all over the world and help them on their journey of learning foreign languages in a comfortable and enjoyable environment. We are going to have a 20-30-minute trial lesson during which we can get to know each other, set expectations towards the lessons and schedule the timetable. The next step is simple - we start learning the language of your choice! As simple as it is :) During the lessons we will focus on making you speak even with the limited vocabulary because speaking is the key to learning a new language quickly and in a fun way! Cannot wait to receive your in-mail and help you on your journey to learn and speak a foreign language. 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I've had students of all ages, from pre-school kids to senior generation, and I feel comfortable working with both beginners and those who are eager to take their learning process to a new level. In my classes I encourage you to talk in the language we’re studying as much as possible, putting every single bit of knowledge into practice right away. If you’re a Russian-learner, I’d be glad to prove it to you that you can absolutely nail my mother-tongue - and yes, you’ll be able to make a small talk in Russian by the end of the first class even if you’re an absolute beginner! We’ll be focusing on the topics that are most relevant to your goals, while discovering the language and getting to know more about the culture of people who speak it. I offer a short free trial class, for us to give each other a smile and discuss our teaching pattern, in order to ajust it to your goals and make our lessons the bee's knees :) See you soon! Read more

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The theory of plate tectonics describes the widescale movements of the lithosphere of the earth. The model is based on the ideas of continental drift, which first gained acceptance in the early 1900s. The geoscientific community granted the theory even more validity after the notion of seafloor spreading appeared in the late 1950s. Basically, the lithosphere is not whole but instead is separated into either seven or eight major plates, depending on the definition that you use. Every meeting point between plates has its own relative movement, either transform, convergent or divergent. Volcanic activity, mountain creation and earthquakes all occur along these edges, and the plates move laterally relative to one another between zero and 100 millimeters annually (Read and Watson). Tectonic plates have the ability to move because the lithosphere is stronger than the underlying asthenosphere. Variations in mantle density lead to convection, and when the plates move, it is the result of seafloor movement away from the edge, leading to alterations in gravitational forces, and a downward suction at the subduction zones. The forces that the earth’s rotation, in combination with the solar and lunar tidal forces, also have an effect on the movement of the plates. However, researchers still debate the relative significance of each Scientists did not always accept the reality of continental drift. As late as the ealry 1900s, geologists made the assumption that the major features of the earth were fixed, and that the majority of geological features like mountain ranges or basin development were attributed to vertical movement in the crust. The explanation for this was a contracting planet losing heat over As early as 1596, researchers observed that the opposing coasts of the Atlantic Ocean have shapes that look as though they fit together at one point (Kious and Tilling). Many theories came out to explain that oddity, but the overweening assumption of a solid, stable crust made it difficult to absorb these proposals. However, the discovery of the heating properties of radioactivity in 1895 prompted a new examination of the age of the planet. In previous estimates, the cooling rate had been set for the radiation of a black body, or an ideal physical body that absorbs all electromagnetic radiation, no matter the angle of incidence or frequency. Knowing that the radioactivity could well have provided a new source of heat, the planet could be much older than a few million years, and the core might still be hot enough to have remained liquid. In 1912, Alfred Wegener presented a theory of continental drift to the German Geological Society on the basis of the research of several theorists in the 1800s as well as his own work. Eduard Suess had posited the existence of the supercontinent Gondwana in 1858, and Roberto Mantovani had proposed the joining of all of the continents into Pangaea in 1889. Both of these earlier researchers suggested that thermal expansion had led to volcanic activity that broke the continent apart, and the continents had drifted apart through further growth of the ripzones, which is where the major oceans now lie. This inspired Mantovani to suggest the Expanding Earth theory which later was seen to be flawed (Scalera and Lavecchia). Frank Bursley Taylor suggested in 1908 that the continents were pulled toward the equator by an increase in lunar gravity during the Cretaceous, making the Alps and Himalayas form. Wegener, though, was the first to formally publish the assertion that the continents had drifted away from one another. However, the fact that he was unable to explain the physical forces causing the drift left his theory still wanting. Today, evidence for continental movements on tectonic plates is widespread. Similar animal and plant fossils appear around different continental shores, implying that they once shared a connection. For example, the Mesosaurus, a freshwater reptile, appears in fossil form on both the coasts of Brazil and South Africa. The Lystrosaurus, a land reptile, appears in fossil form in rocks in Antarctica, Africa and South America, all from about the same time frame. Some earthworm families still appear in both Africa and South America. Another piece of evidence of continental drift is the obvious similarity between the facing sides of Africa and South America. However, those shapes will not always stay complementary. The processes of ridgepush and slab pull are just two physical forces that will continue to push those continents apart, rotating them away from one another. The widespread incidence of permocarboniferous glacial sediments in Arabia, Madagascar, Africa, South America, Antarctica, Australia and India was one of the most significant pieces of evidence for the larger theory of continental drift. The continuous nature of glaciers, inferred from tillite deposits and glacial striations, suggested that Gondwana had actually once been a supercontinent. The striations implied a glacial flow toward the poles from the equator, at least in terms of modern cartography, supporting the idea that the planet’s southern continents had once been in very different places and contiguous with one another However, the fact that Wegener was not even a geologist, along with the fact that he was missing a driving force to explain the movement, meant that continental drift was still a long way had shown that the floating masses sitting on a rotating planet would gather at the equator. Second, masses floating within a fluid substratum, such as icebergs, should have a balance between the forces of gravity and buoyancy, which was not the case throughout the planet. Finally, some of the planet’s crust had hardened while others were still fluid, and the whole surface should have solidified. Because these conditions meant that the contemporary assumptions about continental drift had failed, researchers still refused to accept the theory until geophysicist Jack Oliver provided the first convincing seismologic evidence of tectonics that contained and recast the theory. Beginning in 1965, a series of scientific breakthroughs established plate tectonics as the most viable way to explain the movement of the continents. In 1965, Tuzo Wilson added the notion of the transform faults to the model. This explained the operation of faults in such a way as to make plate movement logical. That same year, the Royal Society of London held a continental drift symposium which officially began the acceptance of the theory within the scientific community. One of the presentations at the symposium covered the calculations that show how the continents on the edges of the Atlantic Ocean would fit to bring the ocean to a close. The next year, Wilson published a paper referring to previous plate tectonic structures, introducing what researchers would call the Wilson Cycle. In 1967, rival proposals were published suggesting the existence of six and 12 plates, respectively. Currently, geologists know that two types of crust exist, continental and oceanic crust.The continental variety is lighter by nature and has a different composition, but both types rest above a “plastic” mantle with much greater depth. At the spreading centers, oceanic crust appears, and this process, coinciding with subduction, causes chaos in the plate system, leading to places with isostatic imbalance. The theory of plate tectonics is currently the best explanation that exists for the drift of the continents. Scientists now believe that tectonic motion first ensued about three billion years ago (Zhao). To gauge the movements of the continents, researchers use different types of quantitative and semiquantitative information. Magnetic stripe patterns show relative plate movements going all the way back into the Jurassic period. The tracks of hotspots provide more absolute data, but they only go back to the Cretaceous period. Older proposals rely on paleomagnetic pole data, but the fact that these only constrain latitude and rotation means that these constructions are not far wrong. Researchers combine poles with different ages within a particular plate to generate polar wandering paths to compare movement of different plates over time. The distribution of various types of sedimentary rock, fossil evidence of faunal habitation and the positioning of orogenic belts takes the case for tectonic movement even further. Current theory suggests that the supercontinent Columbia or Nuna formed about 2 billion years ago, breaking up about 500 million years later (Zhao). About a billion years ago, rodinia is suggested to have formed, containing most of the planet’s land, breaking into eight continents about 600 million years ago. They reassembled into Pangaea but then broke into Laurasia, which became Eurasia and North America, and Gondwana, which turned into the other continents. When two major plates collided, the Himalayas are assumed to have appeared. Before that, they sat under the Tethys Ocean. Today, satellites and ground stations keep an eye on plate movements, with an eye toward predicting coming earthquakes and other disruptions. Kious, W. Jacqueline and Tilling, Robert I. “Historical Perspective.” This Earth: The Story o Plate Tectonics. U.S. Geological Survey. Scalera, G. and Lavecchia, G. “Frontiers in Earth Sciences: New Ideas and Interpretation.” Annals of Geophysics 49(1). Wegener, Alfred. The Spreading of the Continents and Oceans. Braunschweig: Friedrich Bieweg & Sohn Akt. Ges., 1929. Zhao, Guochun. “Review of Global 2.11.8 Ga Orogens: Implications for a PreRodinia Supercontinent.” EarthScience Reviews 59: 125162.

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Let’s learn to understand and use words from these themes: - Family (e.g., cousin, relative, to encourage, to provide) - Community (e.g., to assist, to protect, dentist, plumber) - Celebration & tradition (e.g., thankful, festive, memory, decoration) - Draw a family tree chart together, listing family members and relatives and showing how they are related. Talk about the different traditions, celebrations, and get-togethers in your family. - Go on a community walk or outing, and visit workplaces or community members who assist your community in different ways. Talk with your child afterwards about the different ways these people help your community. Let’s learn to compare and contrast characters in a text. - When reading a story, discuss how two characters are the same or different. You can act out the characters too! Let’s learn to identify key information in charts and diagrams. - Take the time to look at and explain charts, diagrams (e.g., name the different parts in a picture of a dinosaur skeleton) or maps (e.g., see what each symbol on the map’s legend means). Talk about how charts, diagrams and maps can help you understand things. Can your child consistently: - Understand and use words from these themes: - family (e.g., cousin, relative, to encourage, to provide) - community (e.g., to assist, to protect, dentist, plumber) - celebration & tradition (e.g., thankful, festive, memory, decoration) - Compare and contrast characters in a text. - Identify key information in charts and diagrams. Did you know? It can be easy to fill up a child’s library with make-believe and funny stories. Encourage your child to explore a variety of reading materials, including informational texts, early on. This will help him or her to learn and become familiar with ways of writing and communicating information that are not typically found in story books. As your child makes the transition to reading to learn, this will help him or her be more confident and comfortable reading informational texts.

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Learning common constructions for words is one way that third graders can get traction on their spelling and reading comprehension skills. This guided lesson in word structure introduces kids to the idea that most words are made up of smaller words, and provides opportunities to apply this learning with practical examples. For more printable practice with word structure, check out our recommended worksheets. Understanding the function of nouns is a crucial part of reading and writing fluency. This guided lesson focuses on the types of nouns kids are most likely to come across in third grade texts. Designed by our curriculum experts, the lesson provides grammar instruction and examples to support learning. For more practice, see the nouns worksheets recommended to go along with this lesson. Earth Day is a time for raising awareness and appreciation for our environment. It’s also a time for using correct punctuation! With this lesson, your students will use correct punctuation, like commas, quotation marks, and apostrophes. Get your students excited about possessive pronouns with this fun lost-and-found inspired lesson. By talking about items that belong to themselves and their classmates, kids be gain a better understanding of denoting possession. Challenge your students to make their personal narratives come to life with strong action words, feelings, and thoughts. This lesson will help young learners develop their creativity and writing skills. The punctuation mark with which you end a sentence can change the tone of your statement completely. Teach your third grader how to identify these different tones and their appropriate uses with these exercises made just for them. Looking for third grade punctuation help? Look no further than these third grade punctuation resources, sure to liven up your language skills practice. Try the narrative writing lesson plan or the postcard writing activity, both of which provide targeted instruction on punctuation. If you would like to offer your third graders more advanced material, peruse our fourth grade punctuation resources.

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Experiment 9: Rotational Dynamics Translational motion, or motion without rotation, can be analyzed in terms of force, mass, acceleration, velocity, and momentum. Rotational motion is best studied in terms of a corresponding set of concepts. In order, these are torque, moment of inertia, angular acceleration, angular velocity, and angular momentum. In some ways the study of rotational motion is similar to the study of translational motion, but a complete mathematical treatment of rotation is much more complicated. This is particularly true when it is necessary to ascribe vector properties to rotational motion. A number of demonstrations and experiments will be set up to illustrate the basics of rotational dynamics. The similarity to translational motion will be fairly obvious in a few parts of the lab. In others, the motion is complex and the goal of the lab is to describe the motion rather than give a complete physical and mathematical explanation. The procedure in lab is to observe and experience the demonstrations, think about them and answer the questions using diagrams and applicable laws of physics. Part 1: TORQUE Close a door by pushing on the doorknob. Close the door again using approximately the same force but applying it 5 centimeters away from the hinges. Try again by applying the force on the edge of the door in a direction pointing toward the hinges. Summarize and explain your observations. Comment on the difference between force and torque. Part 2: CONSERVATION OF ANGULAR MOMENTUM Part 3: SHAPE AND MOMENT OF INERTIA A heavy mass in free fall does not fall faster than a light mass. The extra weight is compensated for by extra resistance. A heavy mass on a frictionless plane does not slide down faster than a light mass. A heavy ring and a light ring both roll down an inclined plane with the same speed. What about a ring and a disk? Try this with combinations of rings and disks of different masses. Describe the results and give an explanation. It may be helpful to write down an energy equation for the case of 2 rings of different radii and different masses. Also try the energy equation for a ring and a disk of the same radius and mass. Part 4: CONSERVATION OF ANGULAR MOMENTUM (AGAIN) Part 5: PRECESSION OF A SPINNING TOP (GROUP DEMONSTRATION) This is an interesting phenomenon, and a very difficult one to explain. Both torque and angular momentum must be treated as vectors. Torque causes angular momentum to change according to the following equation: To use this equation the direction of a torque vector must be defined. Follow the moment arm with the fingers of your right hand. Then turn your fingers to follow the force. As you do this, your thumb will point in the direction of the torque vector. A bicycle wheel will be set up so that it can be suspended from a rope as it spins. What is the direction of the torque vector for the accompanying diagram? Set the bicycle wheel spinning so that when viewed from the left in the diagram, it is spinning counterclockwise. Release the wheel. What happens? Show the direction of the angular momentum vector.

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Start by explaining that conflict rarely unfolds on an equal playing field. Instead, power and privilege are almost always at play. Tell students that today, they will be talking about power and privilege. Start by asking if any student can explain what it means to have power. After several students have shared their thoughts, tell students that power is all about options, abilities and action. Power gives people options, so they can have choices and make decisions. It gives people the ability to take action, to do things, and to make things happen in the way they want. Ask students to think of someone from their personal life, or a public figure (current or historical), who holds a lot of power. Then, ask students to turn to a classmate and talk about who they identified as having a lot of power, as well as why they think that person holds power (ex. money, status, fame, appearance, etc). After a couple of minutes, call the student's attention back to you and tell them to hang-on to what they discussed with their partners because it will likely be helpful in a couple of minutes. Now, ask if any student can explain what it means to have privilege. Encourage students to participate who did not already provide a definition of power. After students share their thoughts, present the following definition of privilege: Privilege is a right or benefit that is granted to some people and not others, often on the basis of factors that are out of their control (ex. gender or race). Get students to think about examples from their own life where they experience privilege. After a number of students have shared, mention that power and privilege are often talked about together because having more power than others tends to naturally lead to certain kinds of privilege. Explain that a number of factors influence a person’s power and privilege. On chart paper or on the whiteboard, ask students to help you make a list of factors that influence power and, for each factor, identify the high and low power positions (in Canada). Start this activity by sharing one of the factors as well as the high and low power positions for that factor so that students understand what they are being asked to do. Use guided questions to make sure that students have identified all the major factors influencing power, as shared in the READY section. After making the list, explain that in any relationship, conversation or interaction, the people involved can hold equal power (but this is rare), or there can be a power imbalance, where one person is in a higher power position and the other person is in a lower power position. A power imbalance in a relationship can be a result of any combination of the factors identified. Introduce the term intersectionality and explain that different aspects of a person’s identity might overlap to create unique experiences and modes of discrimination. For example, a woman who is Black does not separately manage the challenges associated with being a woman OR those associated with being Black. Instead, she experiences a unique set of challenges associated with being a woman AND being Black. Students might struggle to understand this idea at first so allow them to ask questions and brainstorm ideas together. Now, ask students to discuss whether different types of power are more or less useful in different situations. After listening to students’ opinions, explain that power dynamics are context dependent. For example, whether or not someone’s first language is English will probably not influence their ability to win a race, but it will create a huge power imbalance when they need to express themselves and advocate for their rights. Ask students to reflect on different situations in their life where they might hold different levels of power and how these power differences affect how comfortable, confident, respected, and valued they feel in any given situation. Finally, spend a couple of minutes talking about how power imbalance has the potential to affect relationships. Consider using the following prompts to get the conversation started: - How can you maintain a reasonable balance of power in your relationships? - How is power related to respect? - Are there any unbalanced power structures within our classroom? If so, what factors contribute to this imbalance? How does this imbalance impact our class community? - Can power and privilege be misused in relationships? If so, how? - What action should we take if we notice the misuse of power and/or privilege within our class or school community?

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The National Park Service offers hundreds of free, standards-aligned lesson plans, many of which can easily be used in classrooms anywhere. A great example is this geology lesson plan provided by Craters of the Moon National Monument & Preserve. Written for elementary students in grades three to five, this lesson uses two interactive activities to teach students about the different layers that make up the Earth's structure and aims to convey the idea that the Earth is dynamic rather than static. In the first activity, the class (with direction from their teacher) creates a human model of the Earth in which students role-play the Earth's layers with movements appropriate to each part. For example, depending on the size of the class, one or two students would play the inner core, three or four would play the outer core, and so on through the deep mantle, the aesthenosphere, and the lithosphere. In the second activity, students work in small groups to build a cross-sectional model of Earth's layers using inexpensive household supplies. Together, these engaging activities are estimated to take about 90 minutes of class time. A vocabulary list, background information, and links to additional resources are also included.

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Remember that transcription is a process that produces an RNA copy of the genetic information found in the DNA prior to its expression. This uses an RNA polymerase for the creation of the DNA's complementary RNA strand, known as mRNA. Just like the DNA polymerase, the RNA polymerase synthesizes the complementary strand in a 5' to 3' direction. It starts at the 3' end of the DNA and begins the pairing up of bases just like the complementary base pairing in double-stranded DNA. The only exception for this is that the RNA polymerase pairs up the A of the DNA with a corresponding U for the RNA strand. Thus, for the problem, the products of transcription will be: In the strand below, a mutation occurs at the 8th nucleotide. The nucleotide is deleted. Transcribe then translate the strand to see what happens to the protein. original : 3' - TAG CTG AAT TGC AGT GCC ATC GATG - 5' mutated : 3' - TAG CTG ATT GCA TTG CCA TTG ATG - 5' Frequently Asked Questions What scientific concept do you need to know in order to solve this problem? Our tutors have indicated that to solve this problem you will need to apply the Mutation concept. You can view video lessons to learn Mutation. Or if you need more Mutation practice, you can also practice Mutation practice problems.

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Electrons are an essential part of an atom. Unlike protons and neutrons, valence electrons take part in the excitement of a chemical reaction. Learn how to find the number of valence electrons of any element in this lesson. What Are Valence Electrons? What makes cool chemical reactions work? Remember those fun experiments like making a volcano from baking soda and vinegar or a rocket from Mentos and soda? We wouldn’t have these reactions without valence electrons.Valence electrons are the electrons located at the outermost shell of an atom. Why are these electrons special? Because when two atoms interact, the electrons in the outermost shells are the first ones to come into contact with each other and are the ones that determine how an atom will react in a chemical reaction.Let’s imagine a fast food, drive-through restaurant. We drive through the lane in our car, reach our hands out the window, and the employee reaches out and hands us the food. The whole interaction between the car and the restaurant rests just on the arms of the employee and driver at their windows. The arms of the driver and the arms of the employee are kind of like valence electrons.Let’s look at some examples below to visualize valence electrons. For the oxygen atom, you can see that the outermost shell has 6 electrons, so oxygen has 6 valence electrons. Neon’s outermost shell has 8 electrons. Neon therefore has 8 valence electrons.The shells of an atom can only hold so many electrons. Each shell has a certain amount of subshells (s, p, d, etc) that have a certain amount of orbitals. Each orbital can hold 2 electrons. The first shell has one subshell, s, which has one orbital, so it can hold 2 electrons. The total number of electrons that each shell can hold is: - Shell 1 – has subshell s, which has one orbital. It can therefore hold 2 electrons. - Shell 2 – has subshells s and p. p has 3 orbitals, so can hold 6 electrons. Add the two that subshell s can hold, and we know that shell 2 can hold 8 total electrons - Shell 3 – has subshells s, p, and d. d has 5 orbitals, so can hold 10 electrons. Shell 3 can hold a total of 18 electrons. Take magnesium, which has a total of 12 electrons. If we draw the electrons for magnesium, you’ll have 3 shells. From their positions, we can determine the electron configuration. Aluminum is all the way in the third row, so its electrons occupy the first and second rows fully, and the third row partially. We count from left to right all the way to aluminum, writing each one down as we go. We can write its electron configuration as1s^2 2s^2 2p^6 3s^2 3p^1In ‘1s^2’ the ‘1s’ refers to the first shell’s subshell s, and the ‘2’ refers to the 2 electrons it will be holding. In ‘3p^1’, ‘3p’ refers to the third shell’s subshell p, and the ‘1’ means it’s only holding one electron. Though p subshells can hold a total of 6 electrons, aluminum only has 13 electrons, with the preceding subshells holding the rest of them. There is text written in red – this means that these subshells are hardly ever used. We use this pattern by filling the subshells with electrons, starting with 1s, then, going down to the next arrow, 2s, and then, 2p and so forth until we arrive to the final number of electrons. Did you notice how writing electron configurations can be tedious? What if you have 100 electrons? That means you can be writing for some time. There is a shortcut to electron configuration, and we call this noble gas configuration. Using this shortcut, we can shorten the electron configuration. How is this done? First, you locate your element that you are interested in. Next, you look at the last noble gas that comes before this element. The noble gases are located at the last column of the periodic table on the right most side. Then you put the noble gas in brackets, and then finish the standard electron configuration that come after. This method of writing electron configuration helps narrow down valence electrons. You would do the same with bromine, as argon is also its immediately preceding noble gas. Bromine has 35 electrons. 35 minus 18 is 17, so you would write argon in brackets and follow it with 4s^2 3d^10 4p^5. The highest level is 4, and there are 7 electrons, so the number of valence electrons for bromine is 7.If you do the electron configuration of all noble gases, you will see that except for helium, which has only 2, all noble gases have 8 valence electrons. The electrons that occupy the outermost shell of an atom are called valence electrons. Valence electrons are important because they determine how an atom will react. By writing an electron configuration, you’ll be able to see how many electrons occupy the highest energy level. The electron configuration can be determined from where the atom is located in the periodic table and by using the spdf chart.Luckily, there is a shorter way to write electron configurations called the noble gas configuration. Noble gases will always have 8 valence electrons, except for helium. Valence electrons – the electrons located at the outermost shell of an atomElectron configuration – the arrangement of electrons around the nucleus of an atomSpdf notation – a short, easy format for notating electron configuration using the periodic table and subshells s, p, d, and f.Noble gas configuration – the electron configuration of noble gasses; can be used as a shortcut for figuring the electron configuration After this lesson, you should be able to write the electron configurations for a variety of atoms, applying spdf notation and noble gas configuration.

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Lesson Plan: Equivalent Fractions Using Multiplication Mathematics • 4th Grade This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to multiply the numerator and denominator of a proper fraction by the same number to find equivalent fractions. Students will be able to - use pictorial models to explain how to use multiplication to find equivalent fractions, - use multiplication to generate equivalent fractions. Students should already be familiar with - finding equivalent fractions using different representations, such as number lines, tape diagrams, and area models. Students will not cover - simplifying fractions, - working with fractions greater than 1, - listing factors or multiples.

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Aligned To Common Core Standard: Precursor to Kindergarten - K.G.B.5 How to Match Colors - Colors play an important role in our life. They are best for both decorating and contrasting purpose. Without colors, life can look absolutely meaningless. So, is it not a good idea to learn all about colors? Learn about the color wheel: Take a look at the full diagram of colors that provide an illustration of which colors go together and which don't. Primary colors - The basic Red, blue and yellow are the primary colors. These are the basic colors in the color wheel that cannot be mixed using any other colors. Secondary colors - now comes the secondary colors in the wheel. Green, orange and purple are colors that can be formed mixing the primary colors. Secondary and tertiary colors: The color wheel also has tertiary colors with a combination of secondary colors. Yellow-orange, red-orange, red-purple, blue-purple, blue-green and yellow green . Match primary colors with other primary colors and complementary colors: Also known as the concept of 'color harmony', created when different are combined together to create a pleasing effect. Colors like red, yellow and blue always harmonize. They are bold and eye-catching, and are always in. The basic idea is to stay in the same color family! These worksheets help students identify and match colors together and name colors as well Printable Worksheets and Lessons - Drawing Roses: Step-by-Step Lesson- You will need green and red markers to complete this one. - Guided Worksheet - This worksheet starts working on the following skills: using tables, keys, and legends. - Guided Explanation - It took me a few years to understand that this, in reality, is a pre-graphing exercise. - Independent Practice Worksheet - Here are 10 shapes that need some color. Time to go to town! - Matching Worksheet - Find the color that matches the color of the object. I tried to make these as helpful as possible for students. These are a little bit more fun than most other worksheets. - Color While You Count... - Choose any 6 crayons. Choose a color for each number below. Color the picture according to those numbers. Write the colors that you used for each number in the color key below the picture. - The Days of the Week in Order - Most calendars start with Sunday as the first day of the week. The days then continue in the order shown below. Use the coloring key to color in the picture based on the number of each day. - Color Your Dresser Matching Activity - You will need crayons for this one. Use the color that matches the number key below. - Match the Fish Bubbles - Draw a line to the number matching the answer of the equation in the bubbles. - Advanced Labeling and Spacing Worksheet - There are 3 living things in the picture below. Write the corresponding number of the living things that each sentence describes. - The Next Number - Find the number that comes after all numbers in the picture. - Blast Off By Adding Ones... - Use the color key below to color in the rocket. Make sure to add the 1s first. - Windmills, Shapes, and Colors - Color in each shape using the color key below. - Within 1 : Coloring Worksheet - Color in the picture using the colored using the key below. The numbers in the picture must less than the number in the key. Match the number, or be 1 more or 1 less than the number in the key.

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Knowledge Powerpoint Pt 1 Transcript Knowledge Powerpoint Pt 1 AQA Physics P2 Topic 1 Distance / Time graphs • Horizontal lines mean the object is stationary. • Straight sloping lines mean the object is travelling at a constant • The steeper the slope, the faster the object is • To work out the speed, you need to calculate • Gradient = change in distance (m) / change in time (s) Velocity/Time Graph part 1 • Velocity is speed in a given • Acceleration is the change in velocity per second when and object speeds up. The units are m/s2 • Deceleration is the change in velocity per second when an object slows down. v = the final velocity (m/s) u = the initial velocity (m/s) t = time taken (s) Velocity/Time Graph part 2 • Horizontal lines mean the object is travelling at a • Straight sloping lines mean the object is accelerating or • The steeper the slope, the faster the acceleration or • A curved line means the acceleration is changing. • The area under the graph is the distance travelled. •The acceleration or deceleration of an object can be calculated from the gradient on a velocity – time graph •The speed of an object can be calculated from the gradient on a distance – time graph •The area underneath a velocity – time graph tells you the distance that an object has Vectors and Velocity Quantities which have a direction and size are known as VECTOR • Displacement – distance travelled in a particular direction. • Velocity – speed in a particular direction. • Force – always has a size and direction. • Acceleration – it has size and direction Speed (m/s) = distance (m) ÷ time (s) Acceleration (m/s2) = change in velocity (m/s) ÷ time (s) AQA Physics P2 Topic 2 Forces between objects • A force can change the shape of an object or change its state of rest (stop an object) or its motion (change its • All forces are measured using the unit •A force is a push or a pull. •When two bodies interact, the forces they exert on each other are equal in size and opposite in direction. •For every action force there is an equal and opposite • Whenever two objects interact, the forces they exert on each other are equal and opposite • A number of forces acting at a point may be replaced by a single force that has the same effect on the motion as the original forces all acting together. This single force is the The resultant force acting on an object can cause a change in its state of rest or motion. Force and acceleration Force (N) = Mass (kg) x acceleration (m/s2) •The size of acceleration • Size of the force • Mass of the object • The larger the resultant force on an object the greater its acceleration. • The greater the mass of an object, the smaller its acceleration will be for a On the road Stopping distance = thinking distance + breaking distance Factors affecting thinking 1. Poor reaction times of the driver caused by 1. Age of driver 2. Drugs e.g. alcohol Investigating friction. How much force is needed to move weights on different surfaces? Factors affecting breaking 1. Mass of vehicle 2. Speed of vehicle 3. Poor maintenance 4. Poor weather conditions 5. State of the road 6. Amount of friction between the tyre and the Weight and mass are not the same thing •The weight of an object is the force of gravity on it. Weight is measured in Newtons •The mass of an object is the quantity (amount) of matter in it. Mass is measured in Weight (N) = Mass (kg) x gravity (N/kg) In a vacuum • All falling bodies accelerate at the same rate. In the atmosphere • Air resistance increases with increasing speed. • Air resistance will increase until it is equal in size to the weight of a falling object. • When the two forces are balanced, acceleration is zero and TERMINAL VELOCITY • An object acted on only by the Earths gravity accelerates at about 10 m/s2 Stretching and squashing A force applied to an elastic object such as a spring will result in the object stretching and storing elastic potential energy Hooke’s Law states: The extension of a spring is directly proportional to the force applied, provided 3.0 that its limit of proportionality is not The extension of a material is its current length minus it original length. Force applied (N) = spring constant (N/m) x extension (m) A force is a push or a pull. When two bodies interact, the forces they exert on each other are equal in size and opposite in direction. These are known as REACTION You need to be able to interpret these diagrams and work out the resultant force in each If the resultant force is zero, it will remain at rest or continue to travel at a constant speed. If the resultant force is not zero, it will accelerate in the direction of the resultant force. AQA Physics P2 Topic 3 Work, energy and momentum Energy and work Energy transferred = work done • Work – the amount of energy transferred. Measured in Joules (J) • Power – The rate of doing work. Measured in Watts (W). 1 joule per second is 1 watt. When a force causes an object to move a distance, work is done Use this formula: Work Done (J) = Force (N) x distance moved (m) Example – if a 1kg mass (10N) is moved through a distance of 2 metres the work done is 20J. Work Done (J) Time taken (s) Example – if a 24J of work is done over a 30 second period, the Power would be 24 ÷ 30 = 0.8W Could you work out how much work you have done climbing a flight of stairs? Electrical power and energy A current in a wire is a flow of electrons. As the electrons move in a metal they collide with the ions in the lattice and transfer some energy to them. This is why a resistor heats up when a current flows through. Electrical power (watt, W) = current (ampere, A) x potential difference (volt, V) Energy transferred (joule, J) = current (ampere, A) x potential difference (volt, V) x time (second, s) Distinguish between the advantages and disadvantages of the heating effect of an Useful Heating a Useful in Fires Gravitational potential energy (GPE) Gravitational Potential Energy – The energy that an object has by virtue of its position in a gravitational field When an object is moved up, its gravitational potential energy increases. When an object is moved down, its gravitational potential energy decreases Change in gradational potential energy (J) =weight (N) x change in height(m) Change in gravitational potential energy = mass (kg) x gravitational field strength (N / kg) x change in height (m) When an object speeds up or slows down. Its kinetic energy increases or decreases. The forces which cause the change in speed do so by doing work. The momentum of an object is produced by the object’s mass and The kinetic energy of an object depends on its mass and speed Kinetic energy (J) = ½ x mass (kg) x speed2 (m/s)2 Elastic potential energy (the energy stored in an elastic object when work is done) can be transferred into kinetic Momentum is a property of moving objects In a closed system the total momentum before an event is equal to the total momentum after the event. This is called conservation of momentum. p = momentum (Kg m/s) m = mass (Kg) v = velocity (m/s) • Can you calculate the momentum of an athlete running at a velocity of 5 m/s with a mass of 75 Kg? • If a train is 1200 Kg and is moving at a velocity of 5.0 m/s and collides with a stationary train with a mass of 1500 kg. The trains will move together after the collision. Can you calculate the momentum of both trains before the collision? And show the velocity of the wagons after the collisions? Explosions are good examples of momentum and conservation When two objects push each other apart they also move apart • With different speeds if they have different masses • With equal and opposite momentum so their total momentum is zero If the ice skaters were to push each other away (explosion) from standing still • Momentum A after explosion = mass A x • Momentum of B after explosion = mass B x • Total momentum before explosion = 0 as both skaters were standing still. (mass A x velocity A) + (mass B x velocity B) = 0 When two objects collide the force of the impact depends on 3 factors: • The mass of the objects The longer the impacts lasts the • The change in velocity greater the impact force is reduced • The duration (time)of the impact. When two vehicles collide • They exert equal and opposite forces on each other • Their total momentum is unchanged Crumple zones are designed to lessen the effect of a collision. In a collision the forces change the momentum of the car • In head on collisions the momentum of the car is • In rear end collisions, momentum is increased. Crumple zones increase the impact time. When you are travelling in a car (or on a bike, skis, train etc.) you are travelling at the same speed as the car. If the car stops suddenly, your momentum continues to carry you forward. If you are stopped suddenly, by hitting the dashboard (or ground) you experience a large force, and therefore a large amount of damage. Car safety features: 1. Seatbelts – stretch to increase the time taken to stop, thus reducing the rate of change of momentum and reducing injury 2. Air bags – inflate to increase the time taken to stop, thus reducing the rate of change of momentum and reducing injury 3. Crumple Zones – crumple and fold in a specific way to increase the time taken to stop, thus reducing the rate of change of momentum and reducing injury Use this formula: Force = change in momentum ÷ time If you increase the time you reduce the force. Potential and Kinetic Energy • Kinetic Energy – movement energy • Gravitational Potential Energy – the energy something has due to its position relative to Earth – i.e. its height. Conservation of Energy When energy is transferred, the total amount always remains the You need to be able to use these GPE = mgh KE = ½mv2

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The figure shows a thermometer that has been left outside in the shade on a hot day. What temperature reading does the thermometer give to the nearest degree? We can see that we’ve been given this figure that shows a thermometer, which is a device that can be used to measure temperature. We can notice that at the bottom of this thermometer there’s a reservoir or bulb that’s filled with something red. And this red substance then extends some way up the scale of the thermometer. This red substance is mercury, which is a liquid that expands when its temperature increases. Now mercury expands with temperature in a known and predictable way. So, depending on the temperature of this bulb, the mercury unit will expand a certain amount. And as a result of this expansion, it will rise up the tube in the thermometer. The amount that it expands determines the height that the mercury rises to. And so, the height of the mercury in the thermometer tube indicates the temperature. We can notice that we’ve got a scale drawn on the side of this thermometer. There are big marks on the scale of 5-degree increments. And these marks are labeled with numbers. Then between each of these big marks, there are four of these smaller marks. Since these four small marks separate this five-degree region into one, two, three, four, five smaller regions, then we know that each one of these small marks corresponds to one degree. We also need to take some care over the particular temperature scale that’s being used here. We can recall that there are several different temperature scales, including the Fahrenheit, the Celsius, and the Kelvin scale. Looking at the top of the thermometer, we can see that we’ve got this degree C written on it. The C here stands for Celsius, and it tells us that this thermometer measures temperatures on the Celsius scale. That means that a temperature measured with this thermometer must have units of degrees Celsius. And so, each small mark on the thermometer corresponds to one degree Celsius. In order to read off the temperature in units of degrees Celsius that this thermometer is measuring, we just need to see how far up the temperature scale this red line comes. The line comes up to this height here, which is actually partway between two marks on the temperature scale. Let’s now have a closer look at what’s going on in this region of the thermometer. Looking now at this zoomed-in view, we can see more clearly the height that the mercury rises to. That height is above this small mark, which is two small marks below the 30-degree Celsius mark, and below this small mark, which is one mark below 30 degrees Celsius. Since we know that each small mark corresponds to one degree Celsius, then we know that the upper small mark, which is one mark below 30 degrees Celsius, must be 29 degrees Celsius and the one below this, the lower mark, must be 28 degrees Celsius. Since the mercury reaches a height in the tube that’s between these two small marks, then we know that this thermometer is measuring a temperature that’s between 28 degrees Celsius and 29 degrees Celsius. Since the thermometer scale only has marks at one-degree increments, then the resolution of this thermometer is not great enough to give an answer to more precision than this. That’s okay though because the question is asking us for the temperature reading given to the nearest degree. If we look closely at the height of the mercury in this tube, we can notice that it’s ever so slightly closer to the mark above it at 29 degrees Celsius than it is to the mark below it at 28 degrees Celsius. That means that the temperature being measured by this thermometer must be slightly closer to 29 degrees Celsius than it is to 28 degrees Celsius. This means that our answer then is that, to the nearest degree, the temperature reading given by this thermometer is equal to 29 degrees Celsius.

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According to The Glossary of Education Reform, student engagement “refers to the degree of attention, curiosity, interest, optimism, and passion that students show when they are learning or being taught, which extends to the level of motivation they have to learn and progress in their education.” What is student engagement and why is it important? Research has demonstrated that engaging students in the learning process increases their attention and focus, motivates them to practice higher-level critical thinking skills, and promotes meaningful learning experiences. How do you determine student engagement? Here are a few methods. - Monitor participation. The easiest way to assess the engagement of your students is to simply observe how they participate in the classroom. … - Monitor participation in small groups. … - Gamify participation. … - Pop quiz! … - Ask your students. How might you define student engagement in your classroom How do you know when students are engaged? Indicators of Behavioral Engagement: - Students are alert and listening. - They track the lesson with their eyes. - They take notes and ask questions. - They answer questions on a basic surface level. - They respond promptly to your directions. What are examples of student engagement? Yet a few illustrative examples include school-supported volunteer programs and community-service requirements (engaging students in public service and learning through public service), student organizing (engaging students in advocacy, community organizing, and constructive protest), and any number of potential … What are the benefits of student engagement? Benefits of Engagement: - Learning with peers. - Developing leadership skills. - Making friends. - Learning life skills. - Higher grade point averages. - Learning inclusive practices. - Interpersonal skills. - Having fun. Is student engagement a problem? In addition to impacting readiness to learn, research has found that problems in classroom engagement are associated with negative academic achievement and behavioral outcomes, such as truancy and suspension (Fredricks, Blumenfeld, & Paris, 2004). How do you observe engagement? You will see students… - Paying attention (alert, tracking with their eyes) - Taking notes (particularly Cornell) - Listening (as opposed to chatting, or sleeping) - Asking questions (content related, or in a game, like 21 questions or I-Spy) - Responding to questions (whole group, small group, four corners, Socratic Seminar) What are six ways to engage students? Motivation Matters: Six Simple Ways to Engage Students - Clarify your expectations (often). Students are unlikely to succeed if they do not know what is expected of them. … - Allow for mistakes. … - Give specific, positive feedback (and fewer empty compliments). … - Keep it real. … - Break the cycle. … - Mix your media. What are some key indicators of student engagement? Reviews of previous literature on student engagement suggest that the following behaviors are important indicators of student engagement in face-to-face learning environments [28–31]: learning effort, participation in class activities, interaction, cognitive task solving, learning satisfaction, sense of belonging, and … What is student emotional engagement? Simply put, emotional engagement is a student’s involvement in and enthusiasm for school. When students are emotionally engaged, they want to participate in school, and they enjoy that participation more. Does engagement lead to learning? It is obviously desirable to have an engaging classroom, but it’s difficult to know when engagement is happening and if it is beneficial for learning. Interest and attention are certainly key components of engagement, but certain types of interest and certain types of attention are better for learning than others. How do you ensure students are engaged and learning? Teaching strategies to ensure student engagement - Begin the lesson with an interesting fact. - Exude enthusiasm and engagement. - Encourage connections that are meaningful and relevant. - Plan for short attention spans. - Address different learning styles and multiple intelligences. - Turn lessons into games. - Turn lessons into stories. What does good engagement look like? The goal of engagement (i.e. the one to one direct interactions you have with members) is simple. You’re trying to positively influence the recipient. You want the recipient to feel as appreciated, respected, understood, smart, and as influential as they possibly can. What are the three types of engagement? There are three types of engagement: emotional engagement, cognitive engagement, and behavioral engagement (Appleton, Christenson, & Furlong, 2008; Marks, 2000; Reschly, Huebner, Appleton, & Antaramian, 2008; Skinner, Kinderman, & Furrer, 2009). What is cognitive engagement? Cognitive engagement is defined as the extent to which students’ are willing and able to take on the learning task at hand. This includes the amount of effort students are willing to invest in working on the task (Corno and Mandinach 1983), and how long they persist (Richardson and Newby 2006; Walker et al.

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Is two less than, equal to, or greater than one? In this problem, we’re given two numbers. One of them is written as a numeral, and the other is written as a word. These numbers are two and one. We’re being asked to compare them. We need to choose which one of these three symbols belongs in between the two numbers. In order to be able to compare the numbers, we need to understand what each of the three symbols means. So let’s go through them one by Out of the three symbols, perhaps the two that are trickiest to remember are the two that are similar to arrows. This might be because we use the equal sign a lot more often. Or it could be because the arrows look so similar. It’s easy to confuse them. So let’s remind ourselves what each symbol means. Firstly, it’s important to remember that when we compare two numbers, we always read comparison statements from left to So when we look at the first symbol from left to right, we can see that the part on the left is narrower than the part on the right. If you can imagine making two little towers of cubes and putting them inside the symbol. Less cubes would fit on the left of the symbol than on the right. So if we were to read this symbol from left to right, it represents the statement “is less than”. The second symbol is the opposite way around. Reading it from left to right, we can see that the wider part of the symbol is on the left this time and the narrower part is on the right. Again, a good way of remembering what this symbol means is to imagine our towers of cubes. This time, we can see that more cubes fit on the left than on the right. So the number on the left is greater than the number on the right. Of course, we already know that the equal sign represents “is the same as”. Interestingly, we could still use our tower-of-cubes idea to show that both sides of an equal symbol are exactly the same. Which of these symbols belongs in between two and one? Remember, we always read our statement from left to right. Should we say two is less than one, two is greater than one, or two is the same as one? Let’s build two towers of cubes to prove which number is greater, a tower of two cubes and a tower of one cube. The tower of two cubes is taller than the tower of one cube. So we’ve proved that two is greater than one. So now we know which of our three symbols to write in between the two numbers. Two is greater than one.

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The snake is five times as long as the caterpillar. Pick the model that shows how long the snake is. In this question, we’re being asked to compare two things, the length of the snake and the length of the caterpillar. And we’re going to need to use multiplication to solve this problem. We know this because the question tells us the snake is five times as long as the caterpillar. When we compare two things using multiplication, we call this a multiplicative comparison problem. We have to use multiplication to calculate how long the snake is. When we’re trying to solve multiplicative comparison problems like this, it helps to sketch a bar model. We’re not told how long the caterpillar is. We could use this bar to represent the caterpillar. And we know the snake is five times longer than this. So, the bar representing the length of the snake would look like this: five times the length is the bar representing the Now, we have to pick the model which shows how long the snake is. Let’s look closely at the first model. Did you notice that this cube train has been made using groups of three cubes? How many groups of three are there? One, two, three, four, five, five groups of three or three multiplied by five. So, if the caterpillar is three cubes long, then each of the bars would be worth three cubes. And the length of the snake would be five lots of three. So, this is the model that shows how long the snake is. If the length of the caterpillar is one times three, the length of the snake must be five times three. This model shows three plus five, not three times five. And this model shows two plus three, which equals five. We picked the model which is five times as long as the caterpillar.

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This lesson is part of Understanding Latitude and Longitude, a unit designed for students in upper KS2 and KS3. It can also be taught as a stand-alone lesson. This lesson explains step-by-step how to find the coordinates of a point on a world map using lines of latitude and longitude. In the activity, students are challenged to find the latitude and longitude of 12 points in all four quadrants of a world map. It is differentiated three ways: Easier – Students find coordinates of 12 points in the NE, SE, SW and NW quadrants of the world map respectively. The compass directions are already filled in. Medium – Students find coordinates of 12 points in the NE, SE, SW and NW quadrants of the world map respectively. Harder – Students find coordinates of 12 points randomly distributed across the four quadrants of the world map. Extension – Students are challenged to draw and label 4 more points on to their map. If you like this resource, we would appreciate a review! We will happily send you a free resource in return for a review or useful suggestions/feedback. Contact us at email@example.com. For more Geography resources, check out www.teachitforward.co.uk. Get this resource as part of a bundle and save up to 50% A bundle is a package of resources grouped together to teach a particular topic, or a series of lessons, in one place. Understanding Latitude & Longitude - KS2/KS3 **Understanding Latitude and Longitude** is a Geography unit designed for students in upper KS2 and KS3. The unit contains a sequence of four lessons which are carefully designed to help students understand the key concepts of latitude and longitude and learn the skill of reading coordinates on a world map. The planning overview and topic title page can be downloaded for free [here](https://www.tes.com/teaching-resource/understanding-latitude-and-longitude-ks2-ks3-planning-overview-12391945). Lessons include: L1 – Introduction to latitude and longitude L2 – Finding latitude and longitude coordinates on a world map L3 – Reading latitude and longitude with greater accuracy L4 – Locating world capital cities using latitude and longitude Each lesson includes a presentation and differentiated activities/worksheets. If you like this resource, we would appreciate a review! We will happily send you a free resource in return for a review or useful suggestions/feedback. Contact us at firstname.lastname@example.org. For more Geography resources, check out www.teachitforward.co.uk. It's good to leave some feedback. Something went wrong, please try again later. Very happy with this resource. Easy to use and the kids loved it. Happy days Thank you so much for the review - I'm glad you enjoyed the lesson. If you would like to try another resource for free at some point get in touch at email@example.com. Ed :) Report this resourceto let us know if it violates our terms and conditions. Our customer service team will review your report and will be in touch.

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An addend (also summand) is any of the numbers that are added to form the sum in an addition problem. Together with an operation and equality symbol (in this case addition (+) and equals (=)) they form an addition sentence, or even more generally, an equation, as in the figure below. The addends in an addition problem are terms of the equation. It is important to learn the various parts of an equation, particularly when the equations are relatively simple, to form a basis for learning more complex mathematical concepts. Knowing the vocabulary used to reference the various parts of the equation allows us to more exactly define new concepts while efficiently referencing others. For example, an equation involving subtraction, multiplication, or division have all the same components, with a key difference being the operation used. Once we know the various parts of an addition equation, we can apply it to other operations, and later extend it into working with variables in algebra. Below are some examples that show ways we can practice addition problems. 1. Identify the addends in 3 + 6 = 9 3 and 6 are the addends. 2. Identify the addends in 1.34 + 7 + 3 = 11.34 1.34, 7, and 3 are the addends. 3. Fill in the missing addend in 3 + ? = 9. The missing addend is 6. Identifying same sum addends can also help with learning and practicing the concepts of addition. Same sum addends are the various possible addends that, when added, result in the same same total. Find 3 different combinations of addends that add to 10. - 1 + 9 = 10 - 2 + 8 = 10 - 5 + 5 = 10

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How to say it - /p/ & /b/ sounds Introduction to Consonants Some consonants are spelt with the same letters as the symbols for the sounds; eg. /p/ = 'p' and /b/ = 'b'. This is not always true for consonants; eg. 'j' = /ʤ/, 'y' = /j/ and 'ch' = /ʧ/. Consonants are either voiced or unvoiced. The difference between an unvoiced sound and a voiced sound is that an unvoiced sound just uses air in the mouth, and a voiced sound uses air from the lungs. The air passes over the vocal cords in the neck, making them vibrate, so the sound is louder. This is because the voiced vowel or diphthong makes the previous sound voiced as well so that the sound is easier to say. However, it is more difficult to understand. You have to guess what the word is from the other information. This is what English speakers do. They do NOT say every word exactly and they do NOT need to listen to every sound. They can guess what the word will be in about 0.2 second by listening to the first sound. Introduction to /p/ & /b/ These consonants are spelt with the same letters as the symbols for the sounds, so /p/ = 'p' and /b/ = 'b'. To make these sounds, close your lips tightly, push air against the inside of your lips, then quickly open your lips and mouth. The difference between /p/ and /b/ is that /p/ is an unvoiced sound, and /b/ is a voiced sound. In /b/ the air touches the vocal cords and makes them vibrate. In /p/ the air does not vibrate the vocal cords. Video of Mouth Follow the instructions as they appear in the video.

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Covering the key principles and concepts in the teaching and learning of mathematics in elementary schools, this text provides trainee and practicing teachers with a quick and easy reference to what they need to know for their course, and in the classroom. The entries are arranged alphabetically, and each contains a brief definition, followed by an explanation and discussion, practical examples, and annotated suggestions for further reading. Pupils make errors in mathematics in their written work, in practical tasks, and in their oral responses to teachers’ questions. Errors can be the result of carelessness or procedural slips. More significant, however, are those errors that reveal misunderstandings of mathematical concepts, procedures ...

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Welcome to our adverbs worksheet for kids! Adverbs are an important part of speech that helps to describe how, when, where, and to what extent an action is being performed. In this worksheet adverbs, you will learn about different types of adverbs and practice using them in sentences. Adverbs are important for kids because they help provide more information about verbs, adjectives, and other adverbs in a sentence. They describe how, when, where, and to what extent an action or state of being is being performed or expressed. Adverb activities will benefit your children’s writing, communication, vocabulary, comprehension, and performance on many standardized examinations, particularly the grammar and language arts parts. Our adverb worksheets are helpful for your kids to learn and grow. Download now.

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1: Numbers and Functions - Page ID When we first start learning about numbers, we start with the counting numbers: 1, 2, 3, etc. As we progress, we add in 0 as well as negative numbers and then fractions and non-repeating decimals. Together, all of these numbers give us the set of real numbers, denoted by mathematicians as \(\mathbb R\), numbers that we can associate with concepts in the real world. These real numbers follow a set of rules that allow us to combine them in certain ways and get an unambiguous answer. Without these rules, it would be impossible to definitively answer many questions about the world that surrounds us. In this chapter, we will discuss these rules and how they interact. We will see how we can develop our own “rules” that we call functions. In calculus, you will be manipulating functions to answer application questions such as optimizing the volume of a soda can while minimizing the material used to make it or computing the volume and mass of a small caliber projectile from an engineering drawing. However, in order to answer these complicated questions, we first need to master the basic set of rules that mathematicians use to manipulate numbers and functions. Additionally, we will learn about some special types of functions: logarithmic functions and exponential functions. Logarithmic functions and exponential functions are used in many places in calculus and differential equations. Logarithmic functions are used in many measurement scales such as the Richter scale that measures the strength of an earthquake and are even used to measure the loudness of sound in decibels. Exponential functions are used to describe growth rates, whether it’s the number of animals living in an area or the amount of money in your retirement fund. Because of the varied applications you will see in calculus, familiarity with these functions is a must. Thumbnail: The addition 1+2 on the real number line. (CC BY-SA 3.0; Stephan Kulla);

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Teachers often use reinforcement to teach new skills or to increase appropriate or desired behaviors. Although the ultimate goal is for students to regulate their own behavior by responding to intrinsic motivators (e.g., feeling proud), initially teachers might need to deliver more concrete reinforcers to encourage appropriate behavior and to help students learn how to control their own behavior. When we think of reinforcement, we typically think of what is referred to as positive reinforcement (e.g., giving a student a sticker for completing an assignment, giving a thumbs up for not talking in the hallway). However, teachers can also encourage a student’s acquisition of skills or desired behavior through negative reinforcement. Negative reinforcement should not be confused with punishment, which consists of providing an undesired consequence to decrease a behavior. Positive reinforcement involves providing the desired consequence after a student engages in the desired behavior, which, in turn, creates the likelihood of increased occurrence of the behavior in the future. Ideally, teachers should try to incorporate positive reinforcement into their daily lessons and activities to encourage skill acquisition and desired behavior. Positive reinforcers fall into three categories: tangible, social, and activity In the attached chart, identify appropriate positive reinforcers in the following categories AND grade levels. Your positive reinforcers must be grade-appropriate For each of the three areas, you must identify two reinforcers for each grade level identified. Your total point value for this assignment is 18 points.

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Suffixes are letters added to the end of words to form new words. These can be used to denote one who does something (e.g. reader) or more than one (e.g. adding -s). This worksheet helps kids practice pluralizing words they know by circling the plural words ending with -s. Students must master sentence formation to be successful English learners. After grasping the ABCs and basic words, the next step is to construct sentences using those words. Worksheets like this one can help teach kids how to make sentences; they need to look at the pictures and select the correct noun or verb to complete each sentence. Help your students figure out the plural nouns in Lilliana's checklist. Look at the six objects in this PDF and add 's' to the nouns to make them plural. Show students how words can be tricky and explain how adding an 's' often changes the noun to its plural form. Constructing sentences follows rules. Parts of speech like nouns, verbs, adverbs, pronouns, and prepositions help. This worksheet focuses on prepositions. Explain prepositions to your child, then examine the pictures together and help them complete the sentences.

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Marching Toward Justice exhibit In 1619, Africans arrived in the English colonies with the same status as many early arrivals indentured servants. Over time, because of their physical appearance, their status changed to enslaved, and they lived through all the horrors of the slave industry and its legacy. Some 300 years later, the U.S. Supreme Court ruled that separate schools are inherently unequal, and so began the long process of integration. Marching Toward Justice tells this uniquely American story, starting with the slave trade and ending with school integration. At the heart of this story is the 14th Amendment. Adopted on July 9, 1868, the 14th Amendment was intended to address the injustices African Americans continued to suffer in the Reconstruction era. The amendment declares that any man or woman born in the United States is a U.S. Citizen regardless of race, social status, gender or conflicting state laws. This provision overruled the Supreme Court's decision in Dred Scott, where it held that African Americans weren't and could never become citizens. The amendment further declares that states cannot deny any person in their jurisdiction "the equal protection of the laws." Phrased differently, no state can treat similar citizens differently without just cause. This provision was a response to the state laws that prevented African Americans from enjoying the rights and freedoms their fellow white citizens enjoyed, such as sitting on juries, owning property and moving freely through public spaces. The Damon J. Keith Collection of African American Legal History created Marching Toward Justice to inform the public about the fundamental importance of the 14th Amendment. With more than 200 photographs and primary source documents, it details our centuries-long journey toward and sometimes away from equal justice for all. To learn more about Marching Toward Justice, or to arrange an exhibition at your school, business or community center, contact Professor Peter J. Hammer, (313) 577-0830.

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AQA Computer Science GCSE Programming Concepts - Random Numbers Random numbers get used all the time in programming. This is a fairly specific area of the syllabus. It might come up in an exam, but it's not too tricky to deal with by using some logic if it does. Creating Random Numbers The idea is pretty simple here: use code to create a random number between two limits. This will most likely need to be assigned to a variable. In general you'd only ever be asked to deal with creating an integer. dieThrow <- RANDOM_INT(1, 6) The code above will create the result of throwing a single 6 sided die - it will return a random choice of the numbers 1, 2, 3, 4, 5 or 6. If I wanted to create different ranges of numbers I can simply change the parameters passed to RANDOM_INT(). So, if I need a random number between 1 and 8 (say I'm rolling 1d8) I go RANDOM_INT(1, 8). The way to do this in Python is: # creating random integer dieThrow = random.randint(1, 6) Note the need to import the external function library random. Random numbers aren't included as standard in Python so this really useful library needs to be imported at the top of your code. More Dice and Bigger Numbers! Make sure that you think about random numbers and probability a little before you get confused. If, for example, you want to model the result of the throw of 2 six sided dice (2d6) you need to create each throw randomly and then add the numbers together. This is totally different from creating a random number between 2 and 12 - the probability of rolling a 7 on 2d6 is, for example 7/36 (there are 7 ways to make 7 on 2d6) whereas there is only a 1/36 chance of rolling a 12 on the same dice. diceThrow <- RANDOM_INT(1, 6) + RANDOM_INT(1, 6) It is, of course, entirely possible to pull a random number from a larger set as well. Say we want a random number between 1 and 1000, we'd simply use: randNumber <- RANDOM_INT(1, 1000) I can also use random numbers to simulate a coin flip. All I need to do is say that 0 is a heads and 1 is a tails and then chose RANDOM_INT(0, 1). The harder bit here is using selection to deal with the result. Using Random Numbers with Arrays Random numbers can be used to randomly choose an element from an array. Sometimes this can be exactly what you need. Say I have an array of names and want to choose a random name from the array. I'd do it this sort of way: nameArray <- ["Alan", "Brenda", "Cedric", "Doris", "Edna", "Fergal", "Grace", "H"] randomNumber <- RANDOM_INT(0, LEN(nameArray)-1) theName <- nameArray[randomNumber] The use of LEN(nameArray)-1 is necessary because we always assume arrays are indexed from 0 - unless an exam question says otherwise. The length of the array is 8 but nameArray will cause an error as there isn't anything at nameArray (an index out of range error specifically). We also need to start from 0 and not 1, otherwise Alan (the element at index 0 of the array) can never be chosen. Hopefully random numbers shouldn't cause too many problems. Just use your common sense and you should be OK.

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After the Civil War, Congress attempted to address how to incorporate recently freed slaves into American society and ensure that it gave them the same rights and liberties as white Americans. To guarantee equal rights for African Americans and limit the growth of white supremacist organizations in the South, Congress passed the Civil Rights Act of 1866, the 15th Amendment, and the Ku KLUX Klan Act of 1871 laws. Despite these efforts, the histories of slavery and racism in America proved challenging to overcome, and failing to successfully put these laws into practice increased the Jim Crow system of state-enforced segregation and discrimination against African Americans. The Black Codes were state laws that were established to restrict the …show more content… For example, the Civil Rights Act of 1866 granted freedmen the rights to sue, testify in court, and own property. However, many Southern states disregarded the law and continued to impose their discriminatory practices. The Civil Rights Act of 1866 aimed to establish citizenship rights for African Americans and counteract the Black Codes. Document 2 outlines the success of the act, stating that it was "the first great law of Reconstruction" and was "the basis of civil rights for all Americans." However, the act failed in terms of enforcement, as states could disregard the law and continue to impose their discriminatory practices. While Congress passed laws aimed at granting African Americans citizenship and equal rights, many southern states disregarded the law and continued to impose their discriminatory practices, such as the Black Codes. This highlighted the tension between federal and state power during the Reconstruction era and the difficulties of enforcing laws aimed at promoting equal rights. The 15th Amendment was a significant success in ensuring equal rights for freedmen, as it granted African American men the right to vote. Document 3 outlines the significance of the amendment, as it "granted citizenship and suffrage to African American men and took a significant step toward dismantling white supremacy." While …show more content… The compromise of 1877 resulted in the withdrawal of federal troops from the South, and southern states were allowed to reestablish white supremacy. Document 5 describes the impact of the end of Reconstruction, stating that it "ushered in a period of state-enforced segregation and discrimination" and "represented a significant failure in the fight for equal rights for freedmen." This ushered in a period of state-enforced segregation and discrimination that persisted for decades. And highlights the fragility of the progress made during the Reconstruction era and the ongoing struggle for civil rights in the United States. The end of Reconstruction also marked the beginning of the Jim Crow era, a period of legalized segregation and discrimination that lasted until the mid-20th century. Because During this period, African Americans were subjected to systematic discrimination and violence, and their rights have been severely reduced. The end of Reconstruction was a significant setback in the fight for equal rights for freedmen, and its effects were felt for many years to Click here to unlock this and over one million essaysShow More The 13th, 14th, and 15th amendments had been ratified to ensure equality to any and all former slaves. The first step to equality was the 13th amendment which had abolished slavery in all states and any other territory of the United States but Black Codes had been designed to keep former slaves from being free of subservient labor. The 14th amendment provided what is known as the Civil Rights to all persons born in the United States and the 15th amendment had given voting rights to all male african americans thus allowing african americans to organize politically and eventually hold major offices in government. However, groups like the Ku Klux Klan had been organized to intimidate african americans from voting or being involved politically. The 14th Amendment and the 15th Amendment were soon to follow, which protected former slaves under the law and granted African Americans the right to vote. With the Freedmen’s Bureau and the Civil Rights Act of 1866, the government was also able to support freed African Americans in finding new jobs, pursuing educations, and more in order to help them succeed. The 13th, 14th, and 15th Amendments to the Constitution abolished slavery, granted citizenship to African Americans, and gave them the right to vote. These amendments were a significant step towards equality and helped ensure that African Americans were no longer treated as second-class citizens. The rights granted to African Americans during Reconstruction paved the way for the Civil Rights Movement of the 1960s and After 4 years of war, called the Civil War, between the North and South, the South finally surrendered and all African-Americans were now American citizens and were able to be among the whites. After the Civil War, they turned into a stage of Reconstruction. Reconstruction is the act of building something back up again to its original form, or even better than before. The reconstruction in our society after the Civil War was really important because it helped rebuild the torn down places in the South, it helped support and heal African Americans, and it helped shape new mindsets of the Inhabitants in the United States of America. This is why the reconstruction in our society after the Civil War was important. Though the fourteenth amendment prohibited state governments from discriminating against people because of race, it did not restrict private organizations or individuals from doing so. White southerners determined to strip African Americans of the right to vote established the poll tax and the literacy test. In some cases whites such as the Klu Klux Klan and the Knights of the White Camellia used outright intimidation and violence to undermine the Reconstruction regimes. The Republican Congress responded with the Enforcement Acts of 1870 and 1871 which prohibited states from discriminating against voters on the basis of race and gave the national government the authority to prosecute crimes by individuals under federal law and use federal troops to protect civil rights. Unfortunately, after the adoption of the 15th Amd. (1870), some reformers convinced themselves that their long campaign on behalf of black people was now over, since blacks should be able to take care of themselves with the right to The road to equality for African Americans has always been a bumpy one and still continues to this day. Using hindsight, historians determined that the Civil War and Reconstruction were vital to the fight for equality in the United States, despite the steps that the states took to keep African Americans segregated from society through Black Codes and Jim Crow laws. With the Thirteenth, Fourteenth, and Fifteenth Amendments being written into the Constitution during the Reconstruction period as a result of the Civil War, slaves were finally seen as people rather than property. Though the Reconstruction after the Civil War did not create a society where Black people weren't oppressed, this period in time still made significant progress toward creating a more equal society. The Jim Crow laws were a series of oppressive laws that were enacted during the Reconstruction to target African Americans in the United States. These laws mandated strict racial segregation in public places such as schools, restaurants, and public transportation. They also disenfranchised African Americans by preventing them from voting, serving on juries, and other civil rights. Jim Crow laws also allowed for the enforcement of segregation through police brutality and other forms of violence. These laws were in effect until 1965, when the Civil Rights Acts were passed. Constitution. However, despite the abolition of slavery, African Americans continued to face widespread discrimination and segregation in many aspects of society, including housing, education, employment, and voting rights. The Jim Crow laws, which were state and local laws in the Southern United States that enforced racial segregation and discrimination, were a major obstacle to African American civil rights. In the 1950s, the Supreme Court of the United States made a series of landmark decisions that laid the foundation for the African American civil rights movement. The reality for many African Americans was that they were being prevented from exercising their right to vote and faced violence in order to prevent them from doing so. Some of the most common tactics used against them were lynching and getting shot. The 15th Amendment gave former slaves the right to vote, but only for the men. Although this amendment was difficult to enforce at the time. As W.E.B. DuBois has stated, “The slave went free; stood for a brief moment in the sun; then moved back again toward slavery.” It was aimed to overcome legal barriers at the state and local levels that prevented African Americans from exercising their right to vote under the 15th Amendment (1870) to the Constitution of the United States. The act significantly widened the franchise and is considered among the most far-reaching pieces of civil rights legislation in U.S. history. Many people look back to the civil rights movement to see people like to see people like Martin Luther King, and Robert Williams and so many others that wanted to see change for minorities in America. They fought for their rights every day of their lives like so many others and The Final phase had no real leader and took place from 1877 to 1900. People saw the end of reconstruction and the rise of Jim Crow laws and other forms of institutionalized racism in the South. During this time many of the gains made by African Americans during Reconstruction were rolled back, and segregation and discrimination became more entrenched in Southern Society. This period also saw the rise of the civil rights movement, as African Americans and their allies worked to challenge segregation and discrimination and fight for equal rights under the The freedom in the new society led to more improvements and beliefs on how to make the changed society better. During the period of Reconstruction, three new amendments passed that had to do with the freedom and rights of freed African Americans. The 13th Amendment, passed in 1865, abolished slavery once and for all. Passed in 1866, the 14th Amendment gave everyone who was born in America full citizenship. Lastly, the 15th Amendment said that no citizen can be denied the right to vote because of your race, the color of your skin, or of previous conditions of enslavement. Reconstruction was a monumental era for African-Americans, and for the U.S. as a whole. The Reconstruction era was initially created to gradually abolish slavery and eliminate the racist ways of the South. Even though this was the case, towards the end of Reconstruction, the South showed that Reconstruction didn’t help them develop from their cruel ways by returning to mistreat African Americans At the beginning of the Reconstruction era, African Americans started to have hope that they would finally have a say in the development of their nation. This was due to the fact that immediately when Reconstruction started, Congress sought to protect recently freed slaves by enforcing a civil rights bill and extending the establishment of the Freedmen’s The Reconstruction period, one of the most controversial periods in American history, During the Reconstruction majority of the blacks were defenseless given the new state constitutions were incorporated by different challenges such as prejudiced literacy tests and poll taxes. At the end of the Civil War, the South beaten and there land destroyed, the destruction was tremendous, and the old social and economic order that was established on slavery depleted completely. The Confederate states had to be reformed to their positions in the Union. The free slaves in the south had to be well-defined. The codes imposed a series of restrictions on African Americans, including limits on their freedom of movement and labor, and imposed severe penalties for any violations of these restrictions. The impact of the Black Codes was significant as they effectively re-established a form of slavery under a different name and thwarted the progress of the Reconstruction Era, setting back the cause of civil rights for African Americans for many years to come. The Black Codes of 1863 were a series of laws passed by Southern states in the United States immediately following the end of the Civil War. These laws aimed to restrict the rights and freedoms of newly freed slaves and maintain African Americans' social and economic subordination. The Black Codes had a profound impact on the lives of African Americans, as they effectively re-established a form of slavery under a different name and prevented many former slaves from fully enjoying the fruits of their newfound

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Over The Boxes The worksheet is a handwriting practice sheet tailored for young students learning to write their names. The worksheet prompts the child to identify the starting letter of their name and the total number of letters it contains. There are three different sections for name writing: one with a blank line, another with a label saying “My name is:” followed by a box to fill in, and a third section with individual boxes for each letter of the child’s name. A cartoon character adds a playful element to the page, making the learning process more engaging. This worksheet is designed to teach students how to recognize and write the individual letters of their name. It begins by encouraging awareness of the specific letters their name starts with and the length of their name. The varied sections for writing provide practice in letter formation and spacing within the context of writing their own name. Additionally, breaking down the task into smaller steps, such as placing one letter in each box, helps to build confidence and reinforces the concept of sequencing in writing.

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Roll and Circle Learning Goals: Number Sense, Math Skills, Subitizing, Turn-Taking, Spatial Reasoning, Measurement - Provide student with a handful of small loose parts (ex. beads, dried beans, macaroni pasta, buttons, etc.) and a blank sheet of paper. - In pairs or small groups, have students put their paper on the table and spread out their small materials all over the sheet of paper. - Note: You can put the paper down inside a shallow baking dish if you want to control the loose parts from going everywhere. - Model rolling the dice and identifying the number you rolled. - Demonstrate how to find a group on the paper that matches the number you rolled and circle around it. - Have one student in each pair start by doing the same. Encourage students to point and count aloud to confirm their circled group. - After circling their group, the next student can roll and circle. Students can go back and forth until their are no loose parts left on their sheet! - After students complete the acitivity, encourage them to get creative with new materials and new ways to play. Provide them with a fresh sheet of paper and see what they come up with!

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For some time now, Phaethon, an asteroid, has been perplexing astronomers. When it comes closest to the sun, a long tail of material is visible leaving the three-mile-wide (five-kilometer-wide) rock. However, if Phaethon’s tail consists of usual comet ingredients like ice and carbon dioxide, it should also be visible when the comet is as far away as Jupiter. But it’s not. So, scientists have come up with some theories about Phaethon’s composition that could explain what trails behind when the asteroid passes the Sun. A new study has revealed that the infrared emissions of Phaethon analyzed by NASA’s Spitzer space telescope resemble emissions of meteorites in laboratories, suggesting Phaethon belongs to a rare class of meteorite, of which only six specimens are known. Phaethon’s emission spectrum corresponds to a type of meteorite called the “CY carbonaceous chondrite,” distinguishing it from other well known asteroids like Ryugu and Bennu. This suggests that Phaethon had a unique origin, showing signs of drying and decomposition due to heating, along with a high iron sulfide content. Analyses of Phaethon’s emission spectrum indicated olivine, carbonates, iron sulfides and oxide minerals, all of which supported the space rock’s connection to the CY class of asteroid. The researchers were able to demonstrate how temperatures encountered when passing by the sun might affect minerals in the asteroid, leading to the production of gases and small dust particles that form Phaethon’s tail as it passes by the sun. This research has contributed to a better understanding of the behavior of this mysterious cosmic object. Continue reading about this fascinating discovery here.

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Vectors can be graphically represented by directed line segments. The length is chosen, according to some scale, to represent the magnitude of the vector, and the direction of the directed line segment represents the direction of the vector. For example, if we let 1 cm represent 5 km/h, then a 15-km/h wind from the northwest would be represented by a directed line segment 3 cm long, as shown in the figure at left. A vector in the plane is a directed line segment. Two vectors are equivalent if they have the same magnitude anddirection. Consider a vector drawn from point A to point B. Point A is called the initial point of the vector, and point B is called theterminal point. Symbolic notation for this vector is (read “vector AB”). Vectors are also denoted by boldface letters such as u, v, and w. The four vectors in the figure at left have the same length and direction. Thus they represent equivalent vectors; that is, In the context of vectors, we use = to mean equivalent. The length, or magnitude, of is expressed as ||. In order to determine whether vectors are equivalent, we find their magnitudes and directions.

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Astrophysicists simulate the dark matter that cradles a galaxy. In the early 1930s, the eminent Swiss astronomer Fritz Zwicky noticed something very odd as he was looking to the skies: Galaxies seemed to move around each other too fast. Zwicky was scrutinizing a group of eight galaxies orbiting one another more than 350 million light years away in the Coma Galaxy Cluster. Drawing from early work by Issac Newton and Albert Einstein, he understood the balance of forces necessary to keep the galaxies in this dance. Like a yo-yo swung by a child, they need both the centrifugal force pushing them outward and the string—in this case gravity—pulling them back in. Too much force inward and the system collapses; too much outward and the galaxies fly apart. From a yo-yo to a galaxy, every object in the universe with mass exerts a gravitational pull on other objects. To Zwicky, the galaxy cluster he was observing appeared to have too little mass, and therefore too little gravity, to keep the galaxies from flying off into space. He and his colleagues theorized that these and all galaxies must be dominated by matter invisible to the eye. They called it dark matter. Equipped with an understanding of how gravity works and extensive observations of planets, stars and galaxies, scientists have in fact concluded that less than one-fifth of the matter in the universe is visible. The remainder, dark matter, has no interaction with regular matter except through the force of gravity. Nevertheless, so much dark matter exists in the universe that its gravitational force controls the lives of stars and galaxies. What, then, would dark matter look like if we could see it? A team led by astrophysicist Piero Madau of the University of California–Santa Cruz has taken a substantial step toward answering this question. Using the power of Oak Ridge National Laboratory's Jaguar supercomputer, Madau's team has run the largest simulation ever of dark matter evolving over billions of years to envelop a galaxy such as our own Milky Way. The envelope is known as a dark matter halo. Madau and his collaborators—including Juerg Diemand and Marcel Zemp, both of UCSC, and Michael Kuhlen of the Institute for Advanced Study in Princeton, New Jersey—reviewed the simulation and their findings in the journal Nature. The simulation followed a galaxy worth of dark matter through nearly the entire history of the universe, dividing the dark matter into more than a billion separate parcels. The effort was staggering and involved tracking over 13 billion years the evolution of 9,000 trillion trillion trillion tons of invisible materials spread across 176 trillion trillion trillion square miles. Each parcel of dark matter was 4,000 times as massive as the sun. Hypothetical particles with real gravity Scientists are still trying to determine exactly what dark matter is. Candidates include hypothetical particles such as the neutralino, the sterile neutrino, the axion or some other weakly interacting massive particle. Fortunately, researchers do not need to fully understand dark matter in order to simulate it. All they need to know is that dark matter interacts with other matter only through gravity and is cold, meaning the matter is made up of particles that were moving slowly when galaxies and clusters began to form. Using initial conditions provided by observations of the cosmic microwave background, Madau and his team were able to simulate dark matter through a computer application called PKDGRAV2, developed by a group of numerical astrophysicists at the University of Zurich, who ignored visible matter and focused entirely on the gravitational interaction among a billion dark matter particles. The project had a major allocation of supercomputer time through the Department of Energy's Innovative and Novel Computational Impact on Theory and Experiment program. The simulation used about 1 million processor hours on the Jaguar system, located at ORNL's National Center for Computational Sciences. "The computer was basically just computing gravity," Madau explained. "We have to compute the gravitational force among 1 billion particles, and to do that is very tricky. We are following the orbits of these particles in a gravitational potential that is varying all the time. The code allows us to compute with very high precision the gravitational force due to the particles that are next to us and with increasingly less precision the gravitational force due to the particles that are very far away because the gravity becomes weaker and weaker with distance." Dark matter is not evenly spread, although researchers speculate it was nearly homogeneously distributed immediately after the Big Bang. Over time, however, gravity pulled the matter together, first into tiny "clumps" having more or less the mass of Earth. Over billions of years these clumps were drawn together, a process that continued until they combined to form halos of dark matter massive enough to host galaxies. One lingering question was whether the smaller clumps would remain identifiable or would smooth out within the larger galactic halos. The answer required a state-of-the-art supercomputer such as Jaguar, which at the time of the simulations in November 2007 was capable of nearly 120 trillion calculations a second. Because earlier simulations did not have the resolution to resolve any unevenness, the results appeared to show the dark matter smoothing out, especially in the galaxy's dense inner reaches. Madau's billion-cell simulation, however, provided enough resolution to verify that the earliest forms of dark matter do indeed survive and retain their identity, even in the very inner regions, where our solar system is located. "We expected a hierarchy of structure in cold dark matter," Madau explained. "What we did not know is what sort of structure would survive the assembly because as these subclumps come together they are subject to tidal forces and can be stripped and destroyed. Their existence in the field had been predicted. The issue was whether they would survive as assembled together to bigger and bigger structures." "What we find," he continued, "is the survival fraction is quite high." Madau's team will be able to verify its simulation results using the National Aeronautics and Space Administration's Gamma-Ray Large Area Space Telescope. Launched on June 11, 2008, The telescope will scan the heavens to study some of the universe's most extreme and puzzling phenomena: gamma-ray bursts, neutron stars, supernovas and dark matter, just to name a few. While dark matter particles cannot themselves be detected (direct detection of dark matter is being pursued by large underground detectors), researchers believe that dark matter particles and antiparticles may be annihilated when they bump into each other, producing gamma rays that can be observed from space. The clumps of dark matter predicted by Madau's team should bring more particles together and thereby produce an increased level of gamma rays. A second verification comes from an effect known as gravitational lensing, in which the gravity exerted by a galaxy along the line of sight bends the light traveling from faraway quasars in the background. If the dark matter halos of galaxies are as clumpy as this simulation suggests, the light from a distant quasar should be broken up, like a light shining through frosted glass. "We already have some data there," Madau noted, "which seems to imply that the inner regions of galaxies are rather clumpy. The flux ratios of multiply imaged quasars are not as you would predict with a smooth intervening lens potential. Instead of a smooth lens, there is substructure that appears to be affecting the lensing process. Our simulation seems to produce the right amount of lumpiness." Madau's simulations in less than two years have reshaped the discussion about how our universe is held together. As researchers have access to increasingly powerful supercomputers, their findings could enable them to join their predecessors Newton and Einstein in unlocking the door to some of humankind's most fundamental questions.—Leo Williams Web site provided by Oak Ridge National Laboratory's Communications and External Relations

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Right Triangle Model and the Pythagorean Theorem Help (page 2) Introduction to Right Triangle Model and the Pythagorean Theorem We have just defined the six circular functions – sine, cosine, tangent, cosecant, secant, and cotangent – in terms of points on a circle. There is another way to define these functions: the right-triangle model . Triangle and Angle Notation In geometry, it is customary to denote triangles by writing an uppercase Greek letter delta (Δ) followed by the names of the three points representing the corners, or vertices , of the triangle. For example, if P, Q , and R are the names of three points, then Δ PQR is the triangle formed by connecting these points with straight line segments. We read this as “triangle PQR .” Angles are denoted by writing the symbol ∠(which resembles an extremely italicized, uppercase English letter L without serifs) followed by the names of three points that uniquely determine the angle. This scheme lets us specify the extent and position of the angle, and also the rotational sense in which it is expressed. For example, if there are three points P, Q , and R , then ∠ PQR (read “angle PQR ”) has the same measure as ∠ RQP , but in the opposite direction. The middle point, Q , is the vertex of the angle. The rotational sense in which an angle is measured can be significant in physics, astronomy, and engineering, and also when working in coordinate systems. In the Cartesian plane, remember that angles measured counterclockwise are considered positive, while angles measured clockwise are considered negative. If we have ∠ PQR that measures 30° around a circle in Cartesian coordinates, then ∠ RQP measures –30°, whose direction is equivalent to an angle of 330°. The cosines of these two angles happen to be the same, but the sines differ. Ratios of Sides Consider a right triangle defined by points P, Q , and R , as shown in Fig. 12-9. Suppose that ∠ QPR is a right angle, so Δ PQR is a right triangle . Let d be the length of line segment QP , e be the length of line segment PR , and f be the length of line segment QR . Let θ be ∠ PQR , the angle measured counterclockwise between line segments QP and QR . The six circular trigonometric functions can be defined as ratios between the lengths of the sides, as follows: sin θ = e / f cos θ = d / f tan θ = e / d csc θ = f / e sec θ = f / d cot θ = d / e The longest side of a right triangle is always opposite the 90° angle, and is called the hypotenuse . In Fig. 12-9, this is the side QR whose length is f The other two sides are called adjacent sides because they are both adjacent to the right angle. Fig. 12-9. The right-triangle model for defining trigonometric functions. All right triangles obey the theorem of Pythagoras. Illustration for Problems 12-5 and 12-6. Sum of Angle Measures and Range of Angles Sum of Angle Measures The following fact can be useful in deducing the measures of angles in trigonometric calculations. It’s a simple theorem in geometry that you should remember. In any triangle, the sum of the measures of the interior angles is 180° (π rad). This is true whether it is a right triangle or not, as long as all the angles are measured in the plane defined by the three vertices of the triangle. Range of Angles In the right-triangle model, the values of the circular functions are defined only for angles between, but not including, 0° and 90° (0 rad and π/2 rad). All angles outside this range are better dealt with using the unit-circle model. Using the right-triangle scheme, a trigonometric function is undefined whenever the denominator in its “side ratio” (according to the formulas above) is equal to zero. The length of the hypotenuse (side f ) is never zero, but if a right triangle is “squashed” or “squeezed” flat either horizontally or vertically, then the length of one of the adjacent sides ( d or e ) can become zero. Such objects aren’t triangles in the strict sense, because they have only two vertices rather than three. The Right Triangle Model Practice Problems Suppose there is a triangle whose sides are 3, 4, and 5 units, respectively. What is the sine of the angle θ opposite the side that measures 3 units? Express your answer to three decimal places. If we are to use the right-triangle model to solve this problem, we must first be certain that a triangle with sides of 3, 4, and 5 units is a right triangle. Otherwise, the scheme won’t work. We can test for this by seeing if the Pythagorean theorem applies. If this triangle is a right triangle, then the side measuring 5 units is the hypotenuse, and we should find that 3 2 + 4 2 = 5 2 . Checking, we see that 3 2 = 9 and 4 2 = 16. Therefore, 3 2 + 4 2 = 9 + 16 = 25, which is equal to 5 2 . It’s a right triangle, indeed! It helps to draw a picture here, after the fashion of Fig. 12-9. Put the angle θ , which we are analyzing, at lower left (corresponding to the vertex point Q ). Label the hypotenuse f = 5. Now we must figure out which of the other sides should be called d , and which should be called e . We want to find the sine of the angle opposite the side whose length is 3 units, and this angle, in Fig. 12-9, is opposite side PR , whose length is equal to e . So we set e = 3. That leaves us with no other choice for d than to set d = 4. According to the formulas above, the sine of the angle in question is equal to e / f . In this case, that means sin θ = 3/5 = 0.600. What are the values of the other five circular functions for the angle θ as defined in Problem 12-5? Express your answers to three decimal places. Plug numbers into the formulas given above, representing the ratios of the lengths of sides in the right triangle: cos θ = d / f = 4/5 = 0.800 tan θ = e / d = 3/4 = 0.750 csc θ = f / e = 5/3 = 1.667 sec θ = f / d = 5/4 = 1.250 cot θ = d / e = 4/3 = 1.333 Find practice problems and solutions for these concepts at: Trigonometry Practice Test. - Kindergarten Sight Words List - First Grade Sight Words List - 10 Fun Activities for Children with Autism - Grammar Lesson: Complete and Simple Predicates - Definitions of Social Studies - Child Development Theories - Signs Your Child Might Have Asperger's Syndrome - How to Practice Preschool Letter and Name Writing - Social Cognitive Theory - Curriculum Definition

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Add To Favorites Test force, motion, and friction. Build an adjustable roller ball race track with a cardboard box. During a unit of study on gravity, ask students to define friction. Have students think of everyday experiences involving force, motion, and friction. Talk about how friction acts upon moving objects to slow them. In small groups, students design roller ball race tracks from recycled cardboard boxes and construction paper. One way is to turn a box on its side and reassemble it so one side bends down as a ramp. Stabilize the box with masking tape. Cut box top flaps into ramp supports. Create different angles. Cut paper to cover box surfaces. Attach with Crayola School Glue. Air dry. Students mark ramps with lanes and label ramp support levels with Crayola Washable Markers. Ask students to gather balls of different sizes, shapes, and surface textures. Mold balls with Crayola Model Magic. To vary the weight and texture, add aquarium gravel. Air dry overnight. Cut different surfaces (sandpaper, aluminum foil, fabric) to attach to ramps to vary the friction. Students experiment! Predict rolling speeds of various combinations of balls, ramp levels, and friction surfaces. Create data grids with markers. Use a stopwatch to time experiments. Students record relative or actual ball speeds. Color code data. Students report their findings.

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Acid Teacher Resources Find Acid educational ideas and activities Showing 1 - 20 of 4,907 resources Study Jams! Acids and Bases This video about pH will not leave a sour taste in your mouth! Through clear explanations and a little humor, upcoming chemists will learn the definitions and properties of acids and bases, as well as how pH is measured. This would make an engaging review assignment during a unit on the properties of matter. 5th - 9th Science CCSS: Adaptable Acids and Bases Acquaint your chemistry class with acids and bases by showing this bold and bright PowerPoint. Viewers learn about the characteristics of acids and bases and stop at intervals to answer several questions about what they are learning. Use this on the day that you introduce this topic, and follow it with laboratory exercises in which young chemists observe some of these characteristics up close. 8th - 12th Science Using Environmental Models to Determine the Effect of Acid Rain on an Ecosystem Demonstrate to your middle school science learners how chalk breaks down in a weak acid. Discuss what affects acidic rain might have on ecosystems. Lab groups then choose one of two questions: "How does acid precipitation affect an aquatic ecosystem? 7th - 8th Science Is That Legal? A Case of Acid Rain Develop an environmental case study! Elementary learners discover how a case study is used as an analysis tool. The goal of this activity is to show pupils how techniques of persuasion (including background, supporting evidence, storytelling, and call to action) are used to develop an argument for or against a topic. 4th - 6th Science Color Changes with Acids and Bases Getting back to the beginning of the unit, learners use reactions with red cabbage juice to determine if solutions are acidic, neutral, or basic. This is a straightforward and classic investigation, but what you will appreciate is the detail of procedures provide for both teachers and students. 3rd - 8th Science Reactions of Metals with Water, Acid, and Air Chemistry aces test samples of copper, iron, zinc, and magnesium metals in water, hydrochloric acid, and heat. The assignment is organized and the procedures easily followed. A data table and conclusion instructions are given for junior chemists to record in their science journals. 9th - 12th Science Chapter 15 Review, Section 2: Acid-Base Titration and pH Keep it simple with this chemistry assignment. Learners examine an acid-base titration graph and answer four questions about the data. Then they will balance neutralization equations and calculate molarity for several specific solutions. Give this to your class as homework or a quick review before a quiz on acid-base titration. 9th - 12th Science The Effect of Acid Rain on Limestone Pupils investigate the pH of rain water in this earth science lesson. They collect rain water from their area and explore the pH when lime stone is added, then they will use the data collected to conjecture as to the effect of acid rain on buildings and monuments. 6th - 9th Science CCSS: Designed Simulated acid rain, a dilute sulfuric acid solution, needs to be prepared for this demonstration. After a condensed lecture on acid rain, you will apply the solution to a sample of granite and a sample of limestone. Your young scientists will create a data table in which to record the pH of the acid rain both before and after passing through the stone samples. 5th - 7th Science The Acid Test Learners prepare a test solution whose color changes when an acid or a base is added. They determine whether various household substances are acids or bases and look for patterns in the results. Students determine how their test solution compares to commerical acid-bases testers; and search for other test solutions. 6th - 8th Science An acid/base indicator that's made of blended red cabbage and water is used to demonstrate the various reactions that an acid/base solution goes through when some carbon dioxide gas is added. The best way to add the carbon dioxide is to drop a piece of dry ice into the solution. 3 mins 4th - 9th Science Conjugate Acids and Bases This video introduces students to the concept of Conjugate Acids and Bases. The important point for students to grasp, and Sal does a nice job illustrating this point, is that for every conjugate acid/base pair, the weaker the acid, the stronger its base will be. 17 mins 7th - 10th Science The picture of the DNA double helix provides a logical start to describing how the base pairs match up and how the order codes for a chain of protein molecules. Three billion of these base pairs code for any protein present in your body. Learners will find genes more relevant when they learn a gene is actually the collection of bases that code for a chain of amino acids. 28 mins 10th - 12th Science pH of a Weak Acid In the previous video, Sal outlined what happens when a strong acid is put into reaction with another compound. In this presentation, he describes what happens when a weak acid is introduced. Sal explains why Hydrofluoric acid is much weaker than Hydrochloric acid, and shows how the molecules disassociate themselves from the weak acid much more rapidly than they do in a strong acid during a chemical reaction. 18 mins 7th - 10th Science

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A hot air balloon works by applying these simple principles to air. First, a fan is used to blow air into the balloon, but not enough to fill it up completely. Then, a burner is used to heat up the air inside of the balloon. When this happens, the air molecules in the balloon speed up and move farther apart. This causes the heated air to occupy a larger volume than it did before it was heated. Because the heated air now occupies a greater volume, but still has the same mass, we know that its density has decreased. How do we know this? Remember that density is a measurement that compares the mass of a substance to the amount of volume that it occupies. Hot air balloons float because the volume of the balloon is so large that the entire balloon, including the basket and the people is less dense than the surrounding air.

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Why Lesson Planet? Find quality lesson planning resources, fast! Share & remix collections to collaborate. Organize your curriculum with collections. Easy! Have time to be more creative & energetic with your students! Students practice calculating the slope of a line. They explain how the formula is derived and identify properties that are associated with positive, negative and undefined slopes. They complete an online activity as well. 3 Views 22 Downloads

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Start a 10-Day Free Trial to Unlock the Full Review Why Lesson Planet? Find quality lesson planning resources, fast! Share & remix collections to collaborate. Organize your curriculum with collections. Easy! Have time to be more creative & energetic with your students! Common Idioms 6 In this figures of speech activity, students use their language skills to identify the meaning behind each of the 10 idioms. 7 Views 121 Downloads Figurative Language Packet A definitive resource for your figurative language unit includes several worksheets and activities to reinforce writing skills. It addresses poetic elements such as simile and metaphor, personification, hyperbole, and idioms, and... 6th - 12th English Language Arts CCSS: Adaptable Common Core Teaching and Learning Strategies Here's a resource that deserves a place in your curriculum library, whether or not your school has adopted the Common Core. Designed for middle and high school language arts classes, the packet is packed with teaching tips, materials,... 6th - 12th English Language Arts CCSS: Designed When Pigs Fly: A Lesson Plan on Idioms Not to keep you on pins and needles, but don't jump the gun on this idiom resource. Instead, keep from barking up the wrong tree by previewing the entire resource before beginning. The detailed instructions make presenting the activity a... 5th - 8th English Language Arts CCSS: Adaptable Understanding Idioms Is a Piece of Cake Interpreting idioms is a piece of cake! In groups, learners discuss the meaning of some common English idioms and choose 10 to use in sentences. Then, they illustrate the silly, literal meanings of those idioms and can engage in a fun... 3rd - 12th English Language Arts CCSS: Adaptable

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Electricity and Circuits Students will understand basic properties of Students will understand what is required to complete a circuit. Students will be able to build series and parallel circuits and understand the ween the different circuits. Students will learn about conductors and insulators. Ask questions and state hypotheses that lead to different types of scientific investigations (for example: experimentation, collecting specimens, constructing models, researching scientific There are different forms of energy and those forms of energy can be transferred and stored (for example: kinetic, potential) but total energy is conserved Open the phET simulator by… Open the DC on ly circuit simulator Find a way to make a single light bulb light up with as FEW parts hooked up as possible When electricity flows through wires and makes something work, like a light bulb, it is called a circuit. Sketch your circuit below: What seems to be making the light bulb turn on in your circuit? (what do you based on the simulator?) Make a gap in your circuit. Go to the grab bag and play with the different objects. Find out which objects allow ricity to flow and fill in the data table: Objects that allow electricity to flow Objects that do NOT allow electricity to What do the conductors have in common? What do the insulators have in common? For the next few activities, you need to light up more than 1 bulb at the same time, find a way to hook up your bulbs in a way that if you break the connection at one bulb, ALL bulbs go out. Sketch your new circuit: the rest of the bulbs go out if you break the connection at one bulb? This circuit is called a because the bulbs are hooked up in one long “series” or line. Name somewhere you have seen a string of lights that are also a Second circuit: find a way to hook up your bulbs in a way that if you break the nnection at one bulb, ONLY that bulb goes out. Sketch this circuit: Why do the rest of the bulbs stay lit if you break the connection at one bulb? This circuit is call which has 2 or more single loops connected to the same battery. When 1 bulb goes out in these circuits, the rest of the lights stay on! Name somewher e you have seen many bulbs hooked up to one power source, where one bulb can go ou t without affecting the others. You design toys for a toy company. Your boss wants you to hook up the lights in the toy car you are working on in the cheapest way possibl consideration of the quality of the toy. Which circuit should you use if you want to save money by using fewer parts? Why would this circuit be cheaper? You are an electrician working on a house. What type of circuit should you use for the house so that the owners don’t call to complain about their wiring? Why Experiment with the simulator, see what you can make it do!!! What did you do to make light bulbs glow brighter What did you do to make light bulbs glow dimmer How can you c ause a fire ? (In the simulator… NOT in the real world!) Can you c puppy on fire

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Tracing the Number "Sixteen" In this tracing worksheet, students trace five dotted examples of the word "sixteen". There is tracing only on this page; there is no room for extra practice. 3 Views 1 Download Number and Operations: Place Value If your learners are learning about place value and number value comparisons, this set of engaging activities and worksheets will make your job easy! Scholars use math manipulatives to estimate and then determine how many seeds a colony... 1st - 3rd Math CCSS: Adaptable Literacy Teaching Guide: Phonics You don't have to be a teacher in New South Wales to appreciate this phonics teaching guide. The 73-page packet is packed with information about the principles of effective phonics programs, teaching methods, sequencing, key strategies,... Pre-K - 1st English Language Arts

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