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Language Resource: Nouns, Adjectives, and Verbal Usage Language Resource: Nouns, Adjectives, and Verbal Usage Nouns, adjectives, and verbs are three examples of the parts of speech used to create a sentence. A noun is a word that represents a person, place, or thing. An adjective is used as a descriptive word. Verbs are used in a sentence to describe action. The parts of speech work together to make a logical sentence. Consequently, it's important for a student who is learning English to understand the parts of speech as well as how to use them correctly. Learning tools such as an adjective game or parts of speech challenge can be tremendously helpful to a student's progress. The following contains information on some of the parts of speech and their proper usage. The most simple definition of a noun is that it's a person, place, thing, or idea. Common and proper are two types of nouns often found in sentences. A common noun refers to something general. Girl, playground, dog, and ball are all examples of common nouns. A proper noun refers to a specific person, place, or thing. For example, Mrs. Robertson and Chicago are both proper nouns. There are also plural nouns. Box is an example of a singular noun while the word boxes is an example of a plural noun. In many cases, the noun in a sentence appears before the verb. One example of this is: The boy walked in the park. The noun boy in the sentence appears before the verb walked. Yes, the noun park does appear after the verb in the sentence, but the sentence still makes sense. An example of an incorrect sentence would be to put the noun boy after the verb. Incorrect example: The walked boy in the park. Incorrect example: The park walked in the boy. By reading a sentence aloud, a student can determine whether the noun or nouns in the sentence are used correctly. Another type of noun is a pronoun. A pronoun helps to avoid repetition by referring to the noun in a sentence. One example of a sentence in need of a pronoun is: 'Alexander took Alexander's dog to the vet.' The correct example of pronoun usage is: 'Alexander took his dog to the vet.' The pronoun in the sentence is his and it refers to Alexander. Imagine how many times a person's name would be repeated in a single sentence if pronouns didn't exist? Also, a pronoun must always agree with the noun it is referring to. A correct example of this would be, 'Sally took her doll to the playground.' Since the sentence is about Sally and she is a girl, it is her doll. Incorrect example of pronoun usage: 'Sally took his doll to the playground.' The pronoun his doesn't agree with the noun, Sally. Pronouns can also be possessive. Some examples of possessive pronouns are: mine, yours, ours, hers, his, and its. This is a correct example of possessive pronoun usage: The cat isn't ours it must be theirs. The possessive pronouns in that sentence are ours and theirs. A person learning about nouns can get practice using nouns by trying a fun noun game, a grammar challenge, or taking a quiz featuring nouns. Adjectives in sentences are used for description. The owl flew through the foggy night,' contains the adjective foggy to describe the night. There are also adjectives with multiple meanings. Many students find it helpful to learn the various adjectives with adjective flashcards (PDF). Along with describing the appearance of something, another purpose of an adjective is to describe the size of something. In the sentence, 'The box was filled with large lollipops' the adjective large is describing the size of the lollipops. Once again, the adjective must be in its proper place in order for a sentence to make sense. Correct: 'The white rabbit jumped into its hole.' The adjective is white and it's describing the noun rabbit. The adjective is placed before the noun in the sentence. Incorrect: 'The rabbit white jumped into its hole.' After reading the second example a reader may be wondering, what is a rabbit white? Misused adjectives create confusion for the reader and prevent a student from getting his or her point across. Engaging in practice with adjectives is a great way for students to learn how and when to use them. Also, a game that requires a student to think of imaginative adjectives is another way to get in some practice time. The placement of the part of speech is just as important as the part of speech itself. The purpose of a verb is to be the action word in a sentence. In the sentence, 'The cat ran to its food bowl,' the verb ran is referring to the actions of the cat. There are past and present tenses of verbs, as well. For example: 'Billy is in my history class.' The word is is the present tense verb. Present tense means that the action is happening now and not in the past. Alternatively, the sentence, 'Billy was in my history class' contains the verb was. The word was is known as a past tense verb because the action has already happened. A verb has its proper place in a sentence just like all the other parts of speech. Oftentimes, it's describing the action of the sentence's subject. (The subject refers to who or what the sentence is about.) The sentence: 'My dog jumps into its bed' contains the verb jumps and that word is used to describe the action of the dog. The dog is the subject because the sentence is about the dog. Incorrect: 'My jumps dog into its bed.' When a student reads a confusing sentence like that one, he or she should recognize right away that the verb is in the wrong place. Identifying verbs can sometimes be tricky and it may take some time to become comfortable with using them. A challenging verb quiz or other exercises with verbs can prove helpful to a student who is learning about verbs and how they work. Nouns, adjectives, verbs, and other parts of speech are all designed to work together to form coherent sentences. For example, 'The majestic horse jumped over the fence' contains the above three parts of speech. The adjective majestic, the noun horse, and the verb jumped all combine to help a reader to picture the action happening in the sentence. Furthermore, if two elementary students are talking together one can bring a particular person into the mind of the other by saying, 'Mrs. Smith's new haircut is pretty.' The first student's use of the proper noun, Mrs. Smith, helped the other student to picture the person being referred to. By misusing any of the parts of speech, a person can confuse or frustrate a listener. Consequently, it's important to master the parts of speech. Finally, learning all of the details and exceptions regarding the parts of speech can seem like a challenge. Practice with verbs, adjectives, and nouns is a necessary part of the learning process for a student who wants to grasp the material. In addition, a student who becomes familiar with misused words(PDF) as well as words with several meanings will be better prepared to avoid possible mistakes. After all, the more a student knows about the parts of speech the more he or she will feel able to handle the challenges of understanding words and creating logical sentences.

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When dipping layers are encountered in a borehole, and we have a core sample to study, we know two facts: the dip of the bed relative to the borehole, and the location of the bed below the surface. What we don't know is the strike and the dip direction, because the core sample rotates as it comes out of the hole. It is difficult and expensive to get oriented samples from drill holes, although downhole cameras have greatly improved matters. Two boreholes are sufficient to narrow the strike and dip to two alternatives. Of course, three boreholes define the strike and dip uniquely because we have three elevation points in the plane. In the borehole above, the bedding plane has dip D and intersects the core with angle U. The bed could have all possible strikes, and the range of possible bedding orientations outlines a cone with an apical angle of 2U. If the angle U is significantly different in the two boreholes, the structure is not planar. If the sample occurs at depth h, the possible outcrops of the bed at the surface lie somewhere on a circle of radius r. The radius of the circle is given by r = h Cot D = h Tan U. (You can also solve the problem graphically, by drawing a cross-section as above) Two such boreholes define two circles. In practice it is most convenient to refer depths to a common datum elevation. When we do this, the strike of the plane must be tangent to both circles. This construction requires that the circles be on the same plane. If they're not, then a line tangent to the circles won't be horizontal, and therefore will not be the true strike. Thus all depths have to be calculated with respect to some convenient datum plane. If one circle contains the other, there are no solutions. This most often happens if there is a fault or other structural disturbance between the two boreholes. If the circles intersect there are only two lines tangent to both and both are possible strike directions. If the circles touch, there are three tangents and if the circles are separate there are four. However, in every case only two are possible strike directions. The rule for telling valid strike directions is simple: lines that pass between the circles are not permissible because the bed would have to dip in two directions at once. The dip is always toward the centers of both circles. In practice, and why this technique is useful, is that we can often rule out one of the two strike directions because it does not agree with other geologic data from the area. If we know the structures are upright folds trending 25 degrees, and our strike directions from borehole data are 27 and 84 degrees, the 27 degree strike is much more likely to be correct. We may have two boreholes but only one dip measurement. For example, the critical portion of the core may be too highly farctured in one borehole. Two boreholes allow us to confirm that the structure has the same dip in both and is in fact a plane. If we only have one dip determination, we have to assume the structure is a plane (which may or may not be true). Assume the dip is the same in both the known and the unknown borehole and proceed as usual, but be careful in applying the results. 1. Given the borehole data, find the possible strike of the marker bed encountered in each borehole. We also know that regional structural trends are as shown. 2. By construction or calculation, find the radii of the circles where the bedding plane might intersect the surface. 3. Construct the circles. 4. Draw the possible strike orientations (you already know the dip). In this case direction b is most likely to be the strike direction. It may happen that we have a borehole and an outcrop, but we cannot get an attitude measurement (too massive, too fractured, etc.). We can think of the outcrop as a borehole of zero depth. If we place the datum plane at the elevation of the outcrop, we will have one circle defined by the borehole and a point (or a circle of zero radius) at the outcrop. The strike must pass through the outcrop and be tangent to the circle. 1. We have a single borehole and an outcrop. 2. By construction or calculation, find the radius of the circle where the bedding plane might intersect the datum plane at the elevation of the outcrop. 3. Construct the circle. 4. Draw the possible strike orientations. Created 17 March 1999, Last Update 31 January 2012 Not an official UW Green Bay site

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sums will set you free how to teach your child numbers arithmetic mathematics equality and equations Before proceeding with this page, make sure that you are familiar with ‘equality’ or ‘same as’, the first page on equality. When dealing with equations, the essential and vital factor is to keep both sides balanced. Two blocks equals two blocks: Whatever is done to one side, must be done to the other side - add, subtract, multiply, divide, double, square, or turn inside out - must be done to the other side. adding - addition - in balance taking away- subtraction - in balance multiplying - multiplication - in balance dividing - division - in balance At times, making sure that the two sides are in balance can be complicated, but you always have a remedy - check what you are doing with small numbers and see whether the two sides are, in fact, still in balance after your actions. Numbers can be referred to as constants. When we don’t know what a number is, a variable can be used. That is, we know there is a number, but we don’t yet know what it is. All manner of symbols can be used for variables, usually starting with the lower case alphabet, but eventually you may come across Greek letters, German gothic letters, made-up symbols, or even words. So x, y, teacup, or pink balloon could all be used as variables. While it is common to talk of constants and variables, it is important to realise that constants are also a form of variable. ‘One’ can mean one elephant, one galaxy, or the one drawing pin you just sat on. Always remember, there is nothing ‘special’ about numbers. They are just more words used by humans as they seek to commmunicate about, and to become masters of, the known universe. Before immersing yourself in this section, you might want to study, or re-study, any or all of the following pages: Equations often will include several variables and operations. (Operations are actions done to numbers and include adding, subtracting, dividing, squaring - multiplying a number by itself.) Supposing you have the following equation, (2 + 5² - 1/4) ÷ 3 = x, and you want to find the value of x. Yes, you can work it out using lots of blocks but that takes quite a while and isn't very convenient a lot of the time. So what to do, where to start with teasing out a value for x. This is where BODMAS comes in, an acronym for No, algebra is not particularly complicated. Instead of using numbers, you merely use letters or combinations of letters and numbers, or should that be numbers and letters. Note that, in algebra, 2 x a is written as 2a. Another example is 3 x a is written as 3a. 7b is the same as 7 x b. Thus two blocks equals two blocks, and a = a, and 2b = 2b. Or you may have two equations, one telling you that b = 3c, and the other that c = 4. Believe it or not, by this time you are already doing simultaneous equations (two equations and one ‘unknown’). Here are some simple algebraic sums: They call this sort of thing simplifying equations. The prime objective is usually to isolate one element of the equation and express [describe it] it in terms of the rest of the equation. As has already been discussed, the important thing is to keep the equation in balance. The next section takes two nicely complicated equations and shows you how to isolate one element. This is called transformation - you tranform an equation from say, a +b = c, into a = c - b. You might think that I would build up through lots of simple equations, but this way, you will see just about every trick in the book applied to isolating an element, while maintaining the balance of the equation. If you can tackle these two, you can approach almost anything with confidence and fun. This is the way I go about such things, but some people may prefer to go slowly through myriads of graded examples, climbing step by step up the stairs. Here, we go up the lift and balance out of the high wire! Remember, it’s all about balance. What you must do is to keep rigorously to the rule that, “what you do to one side, you must do to the other side” - and not to part of one side, but to the whole of the side. An equation can be thought as, for instance, a shorthand question about a particular (scientific) situation. For instance, if a string is 10 cm long, how quickly will a pendulum swing? But sometimes the equation, or shorthand question, has the wrong object as the subject of the sentence. Maybe you know how fast the pendulum is swinging, and you want to know the length of the string. Here the question has been rearranged. But to calculate the value of one variable (string length, pendulum swing time), the mathematical sentence, or equation, will have to be rearranged. Finding the answer you want is called ‘transforming the equation’. Take the Pendulum Equation. This equation describes mathematically how long a weight on the end of a string (the pendulum) takes to swing back and forth once (its period of oscillation). how a pendulum swings But the pendulum cannot go straight down because it is constrained by the pendulum string. When the pendulum reaches its lowest point, where the pendulum line is vertical again, it cannot stop immediately. There is enough energy for the pendulum to keep moving. And it does so until the pull of gravity is equal to the energy in the moving pendulum. At this point, the pendulum falls back earthward. This we see as the pendulum swinging back and forth. If there is no friction where it is attached to its suspension point and there is no wind resistance to the pendulum’s, this would continue forever. Here is the simple form of the Pendulum Equation: Each letter stands for one of the variables in how a pendulum moves. In the simple pendulum equation, the bob (the lump at the end of the string that swings) is assumed to have no mass. T = period in seconds. The period is the time taken during for one full swing, or oscillation, of the bob back and forth. The bob moves away from its starting point and returns to it. L = length of the pendulum arm [or string] in metres. π = the constant pi, whose value is 3.14159... and so on. Pi is used in geometry calculations involving circles and arcs. g = acceleration due to gravity. An average value for g on Earth is 9.81 m/s². And now let’s delve into the nitty-gritty of the equation. We rearrange the equation. This takes are a number of And here follows the more orthodox method of rearranging this equation. abelard is of the opinion that it is not so easy to understand: The resitor equation is another tricky mathematical animal to tame. But why is there a resistor equation, and why on Earth someone might want to use it? Here is some fairly easy explication, but you can skip it if your head starts to go fizz. A resistor is an electrical element found in almost every electronic circuit. Resistors, as the name suggests, impede current flow and they are used to control the way current courses through the circuit. Their resistance is measured in ohms (symbol Ω). Because most resistors are too small to display figures or letters, their ratings are displayed by colour-coded bands. The behaviour of an ideal resistor is defined by Ohm’s law, “current, I, is directly proportional to voltage, V, for a metal conductor, R, at a constant temperature”, or mathematically: I=V/R [we have rearranged Ohm’s law, V=IR, to match the definition just given]. Ohm’s law will be referred to later on when we explain the resistor equations (yes, there is more than one version). Resistors can be combined by connecting together in in series or in parallel, or in a combination of these ways. This can be helpful if you do not have a resistor of the exact value needed as the values combine.. Often, when building electronic (or electrical) devices, it is necessary to calculate the voltage, or the current being used, or the resistance in the circuit, so that the electronic elements both work, and do not burn up and fail. The resistor equation is used to find out the combined resistance of several resistors in a circuit. This is when resistors are linked one after the other, in a series. Their total equivalent resistance is found by the equation, Req = R1 + R2 + ... + Rn . Finding the value of one of the resistors in the circuit is just a matter isolating that resistor by subtraction. Thus, to find R1 in the equation Req = R1 + R2 + R3, subtract R2 + R3 from each side : connecting in parallel Resistors which connected together so they are in paralleleach have the same potential difference, or voltage. To find their total equivalent resistance, this equation is used: Now supposing the circuit has two resistors in parallel, the equation will be . Find R2, what is R2? Now this is quite tricky to do, we use several mathematical tools which have already been described on other related pages at abelard.org. The mathematical tools are highlighted here in yellow, if you click on them you will be taken to the relevant section of that page. |sums will set you free includes the series of documents about economics and money at abelard.org.| |moneybookers information||e-gold information||fiat money and inflation| |calculating moving averages||the arithmetic of fractional banking| |You are here: how to teach your child number arithmetic mathematics - equality and equations < sums will set you free < Home |about abelard||memory, paranoia & paradigms||francis galton||france zone||memory & intelligence||loud music & hearing damage||children & tv violence| |information||abstracts||briefings||news headlines||news archives||latest| email abelard at abelard.org © abelard, 2009, 11 october the web address for this page is http://www.abelard.org/sums/teaching_number_arithmetic_mathematics_equality_and_equations.php

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Communicative Language Learning (CLL) - CLL seeks to bring students beyond grammatical competence. - Students need to decode language and manipulate it in private dialogue. - This leads to communicative competence. Students must listen to a series of letters and then think of a meaningful phrase which uses each letter as the first letter of a word. The order in which they use the letters is not important. For example, given - A D I F , students might produce: - A day in France - Fantastic dreams are incredible - I ate David's fruit 2. Numbers and sizes ratios (From 'Grammar Activity Book' published by CUP) This activity focusses on general knowledge and guessing numbers and size. Learners then have the chance to produce their own version of the activity. - Put learners into groups of 2 or 3 - Learners look at comparisons on the board or in a handout and discuss how big the difference is between them - They then match the comparison to a ratio - Then they write a sentence expressing the ratio The world's tallest man is 2.5m tall. The world's shortest man is 0.5m tall. The ratio is 1 : 5. The world's tallest man is five times as tall as the world's shortest man. The age of the Egyptian pyramids v the age of the Aztec pyramids - 1 : 2. Aztec pyramids are twice as old as Egyptian pyramids. Number of rows on a chess board v number of squares - 1 : 8. There are eight times as many squares on a chessboard as rows. Other examples you could give: - Number of circles on the Olympic flag / number of circles on the Japanese flag - Paris, distance from London / Athens, distance from London - World's highest mountain / world's highest waterfall - Population of London / population of Mexico City - Number of countries bordering Spain / number of countries bordering the USA - one mile / sixteen kilometres The purpose of this activity is to get learners to think logically and critically, to use their general knowledge and to practise comparative forms. 3. Question to question Sometimes we answer one question with another question, rather than giving a direct answer. Why do we do this? - for clarification - because we don't know the answer - to show interest - to stall - I'm sorry, what did you say? - What do you mean? - Could you repeat that? - Why do you ask? - Don't you believe me? The purpose of this activity is to teach functional language, to practise intonation and question forms, as a confidence booster, and to have fun! Students create a paired dialogue so that each line begins with the next letter of the alphabet. e.g.: - Ahmed, how are you? - Bad, really bad! - Come on, it can't be that bad! - Do you think I'm joking? - Everyone knows you're a joker. For higher level students, you could combine 'alphabet dialogue' with 'question to question'. The purpose of this activity is as a warmer, a confidence booster, to practise real time speaking using colloquial language, and to practise sentence starters. In this activity, learners look at a text which contains nonsense words and try to make sense of it from a grammatical perspective. It is good for helping students with their 'decoding' skills and gives great opportunities for creative language use. An example of a nonsense text: - What is a sloobie? - What does it do?

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If you're seeing this message, it means we're having trouble loading external resources for Khan Academy. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. In this tutorial, we will learn to describe situations using mathematical expressions, and consider the effect of using parentheses in the outcome of those expressions. This word problem can be solved by constructing a numerical expression. Can you help? We bet you can! So maybe parentheses don't seem like a big deal? Check out this problem and the difference in the answer when you work it without the parentheses. Wow. Solve multi-step expressions with parentheses. Place parentheses in an expression to make the expression equivalent to a given number. Interpret written statements, and write them as mathematical expressions. Practice changing expressions from words to math. Practice creating expressions with parentheses from real-world contexts.

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Sampling Distributions for Means The "Central Limit Theorem." This theorem -- which involves averages computed from random samples of data -- is described below. The basic setting is as - A population; each unit in the population has a quantitative value (the variable) associated with - Parameters: The mean m and standard deviation s for the population of values are - A simple random sample. n units are randomly selected from the population in such a way that all possible samples are equally likely to be the selected sample. - Statistics: The mean x-bar and standard deviation s for the sample are statistics. They are used as estimates of the parameters. Statistics are variables. The sample mean x-bar is the focus here. It is a variable (each random sample results in a different sample mean); as such it has a distribution. - The mean of this distribution is m. - The standard deviation of this distribution is s/sqrt(n) (where sqrt(n) means "square root of n"). - The central limit theorem describes the pattern of variability. The distribution of x-bar is approximately normal. The quality of the approximation depends on two factors: - How close to normal the population distribution is. The closer, the - How large the sample size is. The larger, the better. Avoid using this result for situations in which the combination of both nonnormal data and small sample size are present. From here link to worksheets.

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A-level Mathematics/Edexcel/Mechanics 2/Particle Kinematics Kinematics of a particle moving in a straight line or plane Projectiles are objects, like cannonballs, that move freely under gravity along a curved. When dealing with projectiles in M2 we make a number of assumptions: - There is no force acting horizontally on the particle (such as air-resistance). - The only force acting vertically on the particle is gravity. The key to understanding projectiles is to consider the particle in two dimensions, let's call them x and y. The in the x direction, the particles motion is unchanged (because there is no air resistance) and in the y direction, the particle is accelerating due to gravity. For example, a penny which is thrown horizontally from the top of a building will continue to move away from the building as it falls (horizontal motion does not stop as the velocity of the coin increases, it just becomes less noticeable). The hardest part of most questions involving projectiles is resolving the particle's velocity into the x and y plane. For any angle at which a particle is projected the horizontal component is given by and the vertical is given by . This makes sense, as if you have a particle projected at 90° to the horizontal, then the vertical component is given by (which is simply V) and the horizontal component by - or 0. Similarly if our particle is projected at 0°, then our horizontal is V and our vertical is 0. Once the particle is in motion, you can solve equations separately on the x and y directions. So for example you could use the equation to work out how fast the particle is travelling vertically after it hits a wall 5 metres away.

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What Is a Tsunami? A tsunami is a series of waves generated by an impulsive disturbance in a body of water such as a lake or ocean. The disturbance is typically a fault displacement. Less commonly, the displacement results from a landslide (into or below the water surface), volcanic activity, or rarely from a meteorite impact. It typically takes a large earthquake (magnitude >7.0) to generate a damaging tsunami in the near-field and a great earthquake (magnitude >8.0) to generate a tsunami in the far-field. The height of a tsunami ranges from centimeters to more than tens of meters and depends on the initial disturbance and the bathymetry of the seafloor over which the waves travel. The waves are very small in deep water, but grow in height once they move into shallow water. The velocity at which the tsunami travels away from the source depends on the water depth. A tsunami in deep water (≥4 km) is about as fast as a jetliner (700-800 km/hr) and slows to the speed of a car (60 km/hr) in shallow water. For example, a tsunami originating in the central Aleutian Islands near Alaska would arrive on the Hawaiian shores in about five hours. Such tsunamis, originating far from where it runs ashore, are commonly referred to as “far-field” tsunamis, which allow at-risk communities several hours to evacuate if the warning is received promptly. However, a tsunami triggered by an event close to shore (e.g., an earthquake associated with the Cascadia subduction zone), would reach communities in low-lying coastal areas in a few minutes, allowing for little time to warn and evacuate. When the tsunami originates close to the at-risk community, it is termed a “near-field” tsunami. For the near-field tsunami, people need to recognize the triggering earthquake as their warning to evacuate. Tsunami arrival times can range from minutes to many hours. The report mainly discusses the near- and far-field tsunamis (at either extreme end of the arrival time range) because of the unique challenges they pose to the warning and preparedness efforts. However, a tsunami can be triggered by an earthquake that is only weakly felt onshore, yet may arrive in under an hour. Such events are also considered and mentioned because they heighten the challenges associated with preparing and warning the public. probably triggered by earthquakes, account for much of the known tsunami hazard along the U.S. Atlantic and Gulf coasts, and in southern California (Dunbar and Weaver, 2008). Seismically active faults and the potential for landslides in the Caribbean pose a significant tsunami risk for that region (Dunbar and Weaver, 2008). Tsunami hazard zones of U.S. coastal communities contain thousands of residents, employees, and tourists, and represent significant economic components of these coastal communities (Wood, 2007; Wood et al., 2007; Wood and Soulard, 2008). The economic and social risks from tsunamis grow with increasing population density along the coasts. To reduce societal risks posed by tsunamis, the nation needs a clear understanding of the nature of the tsunami hazard (e.g., source, inundation area, speed of onset) and the societal characteristics of coastal communities (e.g., the number of people, buildings, infrastructure, and economic activities)

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After studying the chapter you might find it useful to attempt these Multiple Choice Question Quizzes to assess how well you understood the topic. A sequence refers to a list of numbers with some inherent pattern. General term of a sequence, generally written as an is an expression that for different values of ‘n’ gives different terms of the sequence. A sequence of the type a,a+d,a+2d,a+3d,… is said to form an AP. Each term differs from the previous one by a fixed value called as “common difference”. a and d are usually used to denote first term and common difference respectively. nth term of an AP is given by an=a1+(n-1)dThe tutorial will show you how to compute the sum of the first n terms of an AP 3 terms in an AP are – a-d,a,a+d 4 terms in an AP are – a-3d,a-d,a+d,a+3d And so on. mth term from the end of an AP : It is the (n-m+1)th term from the beginning. Alternately, we can reverse the AP, and consider the first term and common difference of the new AP as last term and negative of common difference of the old AP. If a constant is added, or subtracted, or multiplied or divided from every term on an AP, the resulting sequence is still an AP. if a,b,c are in AP, then b is said to be arithmetic mean of a and c. Equivalently, if 2b=a+c, then a,b,c are in AP. If between a and b we are to insert n numbers A1,A2,A3,….,An such that a, A1,A2,A3,….,An form an AP, then A1,A2,A3,….,An are called n Arithmetic Means. A sequence of the type: a,ar,ar2,ar3,… is called a GP. In a GP, the nth term of a GP is given by: an=arm-1 The tutorial will show you how to compute the sum of first n terms of a GP. When r=1, the GP can be treated as an AP, and clearly the sum of first n terms then is “nXa”. Similar to an AP, mth term from the end is (n-m+1)th term from the starting. A GP of 3 terms : a/r,a,ar A GP of 4 terms:a/r3,a/r,ar,ar3 And so on. If all terms in a GP are multiplied or divided by the same number, or are raised to the same power, then the resulting sequence is still a GP. If a,b,c are in GP then b2=ac and b is called the GM of a and c. Conversely, if b2=ac, then a,b,c are in GP. Sum of infinite terms of a GP: If -1<r<1, then GP is said to converge, that is to say that sum of infinite terms of such a GP tends to a constant value. If a sequence is in AP, then the sequence obtained by taking the reciprocal of every term in the sequence forms an HP. That is if a,b,c,… form an AP, then 1/a,1/b,1/c,… form an HP. Let a,b,c form an HP. Then clearly, 1/a,1/b,1/c form an AP. b is called the Harmonic Mean. Problems related to HP are generally solved by converting it into an AP. NOTE: Let a,b be two positive real numbers. Then AM X HM=GM2. Q: What is the common difference of an AP whose nth term is xn+y? Q: If the sum of n terms of an AP is 2n2+3n, what is the kth term? Q: If am=n and an=m, what is ap? Q: If the sums of n terms of two arithmetic progressions are in the ratio 2n+5:3n+4, then what is the ratio of their nth terms? Q: If sum of n terms of an AP is 3n2+5n then which of its terms is 164? Q: If sum of first p terms is q and sum of first q terms is p then what is the sum of first p+q terms ? Q: If four numbers are in AP such that their sum is 50, and the greatest number is four times the least, then what are the numbers? Q: If n arithmetic means are inserted between 1 and 31 such that ratio of first and nth mean is 3:29, then what is the value of n? Q: If S1 is the sum of an AP of ‘n’ odd number of terms and S2 the sum of terms of the series in odd places, then what is S1/S2? Q: What is the sum of 2 digit multiples of 4? Q: Find the sum of 2+6+18+…+4374. Q: Find the sum of 5+55+555+…n terms Q: Find the sum of n terms of the sequence whose nth term is 2n+3n Q: Find a GP for which the sum of first two terms is -4 and the fifth term is 4 times the third term. Q: Find the least value of n for which the sum of 1+3+9+27+… to n terms is greater than 7000. Q: If a,b,c are in GP, prove that log a, log b, log c are in AP and vice versa. Q: If a,b,c are in GP and x,y are AM’s between a,b and b,c respectively, then prove that x,b,y are in HP. Q: Find the sum to n terms of series 1.2.3+2.3.4+3.4.5+4.5.6+… Q: If a, b, c are in H.P., show that a/b+c, b/c+a, c/a+b are also in H.P. Q: Evaluate: 62 + 72 + 82 + 92 + 102 Q: Prove that (a + b + c) (ab + bc + ca) > 9abc. Q: If a2, b2, c2 are in A.P. show that b+ c, c, c+ a, a + b are in H.P. Q: If the AM between ‘a’ and ‘b’ is twice as greater as the GM, show that a/b = 7+4√3 Q: Sum to the n terms the series, 12-22+32-42+… n is even. Fill up the answers in the Answer Submission Form below this Question-Paper document. Your score will be emailed to you. Answer Submission Form for MCQ Quiz #3 Answer Submission Form for MCQ Quiz #4 You might like to take a look at our other algebra tutorials:

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Compound Words Worksheet 1 Your students will need to put on their thinking caps when they draw a line to match each word in the left column with a word in the right column to make a new compound word. This lesson could be extended by asking students to write five or ten additional compound words on the back of the page. An answer key is included. Grade recommendation: 2 • Common Core State Standards Alignment: L.2.4 Skills: vocabulary | spelling | fine motor skills | making new words Item 3547 | 1 page | Publisher: T. Smith Publishing ©2001 | by Tracey Smith Printing Tip: If a worksheet page does not appear properly, reload or refresh the .pdf file. Click the worksheet preview for the full printable version of Compound Words Worksheet 1. Here are some of the ways our visitors are using this worksheet.• A school board member from Kentucky uses this worksheet for one-on-one tutoring in kindergarten and first grade. • Pearl, a teacher from California writes. "I use this as a warm-up to INSIDES Unit 1 Level E curriculum. We do a mini-lesson on compound words and the following day, this page is a Warm-up review. I then create more difficult pages using a list from a college compound word list from Enchanted and continue as needed."

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Learn something new every day More Info... by email Mantle convection is the process by which heat from the Earth’s core is transferred upwards to the surface. It is thought that heating of the mantle by the core creates convection cells in which hot mantle material rises, cooling as it goes, toward the crust until it reaches less dense material, at which point it spreads out then descends. Similar processes can be observed in any fluid above a hot or warm surface — for example, the atmosphere. Mantle convection is assumed to be responsible for plate tectonics and continental drift as well as volcanism. The Earth consists of three main layers: the core, the mantle and the crust. The core is thought to be composed mainly of iron and nickel, but with a high proportion of radioactive elements; the decay of these elements, along with heat left over from the Earth’s formation, keep the core at a high temperature — thought to be between 5,432 and 10,832 °F (3,000 and 6,000 °C.) Above the core sits the mantle, a layer of hot metal silicate material 1,800 miles (2,900 km) thick, thought to be essentially liquid in its upper reaches, but possibly solid lower down. The topmost layer is the crust, a solid layer of less dense material that floats on the mantle. This consists of oceanic crust — the ocean floor — 4-7 miles (6-11 km) thick and continental crust, 19 miles (30 km) thick. The crust is broken into continental plates, which, throughout geological history, have slowly moved relative to one another, split and joined together, presumably under the influence of convection processes within the mantle. It is thought that where a rising mantle material approaches the crust, the outward spreading motion causes the sections of crust on either side to move apart. The Atlantic Ocean is thought to have formed in this way and the process continues today, with new oceanic crust being formed by mantle material along the Mid-Atlantic Ridge. There are also a number of “hot spots” where mantle material is forming new land at the surface — for example, Iceland and Hawaii. In some areas — like the west coast of South America — sections of oceanic crust can slide under the continental crust and descend deep into the mantle; these are known as subduction zones. While the movement of tectonic plates is well established and supported by observable evidence, the processes going on within the Earth’s mantle that drive tectonics cannot be investigated directly. It seems highly likely that convection processes are at work there, but their exact nature remains unclear. Investigations into mantle convection must use indirect methods, such as the behavior of seismic waves and chemical analysis of mantle material that has been extruded at the surface through volcanic activity. Samples of mantle material taken from different locations have been found to differ chemically from one another. This appears to conflict with theoretical models where convection takes place through the entire depth of the mantle as this should lead to thorough mixing of material, resulting in a chemically homogenous magma. A theory of mantle convection must explain the variable chemical composition of mantle material while agreeing with other observations, and physical constraints, as to the mantle’s structure. In some models, there are distinct layers, with convection taking place in the upper layer, and plumes of material rising from the lower layer. Others involve “blobs” of ancient, deep material floating in the upper mantle. Incomplete mixing of subducted oceanic crust with mantle material may also play a role. Mantle convection is an area of active research and there is, as of 2011, no consensus about the details of the process. One of our editors will review your suggestion and make changes if warranted. Note that depending on the number of suggestions we receive, this can take anywhere from a few hours to a few days. Thank you for helping to improve wiseGEEK!

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Africa Before American Slavery The peoples of West Africa had rich and diverse histories and cultures centuries before Europeans arrived. Africans had kingdoms and city-states, each with its own language and culture. The empire of Songhai and the kingdoms of Mali, Benin, and Kongo were large and powerful with monarchs heading complex political structures governing hundreds of thousands of people. In other areas, political systems were smaller, relying on agreement between people at the village level. Art, learning and technology flourished, and Africans were especially skilled with medicine, mathematics, and astronomy. In addition to domestic goods, they made fine luxury items in bronze, ivory, gold, and terracotta for both local use and trade. West Africans had traded with Europeans through merchants in North Africa for centuries. The first traders to sail down the West African coast were the Portuguese in the 15th century. The Dutch, British, French and Scandinavians followed. They were interested in precious items such as gold, ivory and spices, particularly pepper. From their first contacts, European traders kidnapped and bought Africans to be sold in Europe. However, it was not until the 17th century, when plantation owners wanted more slaves to satisfy the increasing demand for sugar in Europe, that transatlantic slaving became the dominant trade. This material was derived, in large part, from the writings of the International Museum of Slavery. Slavery in America (view timeline) Within several decades of being brought to the American colonies, Africans were stripped of human rights and enslaved as chattel, an enslavement that lasted more than two centuries. Slavers whipped slaves who displeased them. Clergy preached that slavery was the will of God. Scientists "proved" that blacks were less evolved-a subspecies of the human race. The invention of the cotton gin in 1793 solidified the importance of slavery to the South's economy. By the mid-19th century, America's westward expansion, along with a growing anti-slavery movement in the North, provoked a national debate over slavery that helped precipitate the American Civil War (1861-65). Though the Union victory freed the nation's four million slaves, the legacy of slavery influenced American history, from the chaotic years of Reconstruction (1865-77) to the civil rights movement that emerged in the 1950s. In the tumultuous years following the United States Civil War, the federal government was faced with two conflicting challenges: to reincorporate the eleven states that had seceded from the Union, and to define and implement a strategy for ensuring the economic, political, and social rights of newly-freed black Americans. Radical Republicans, with support from the United States Army and the Freedmen's Bureau, led the effort to pass and implement laws that ensured first-class citizenship for blacks. The 14th Amendment to the Constitution (1868) affirmed that black Americans were citizens of the United States and entitled to due process and equal protection under the law. The 15th Amendment (1870) stated that the right of citizens to vote "shall not be denied...on account of race, color, or previous condition of servitude." Conservative white southerners, and their northern allies in the Democratic Party, opposed all efforts to extend human rights to blacks. By 1877, the white southerners who wanted blacks "re-enslaved" had won; the new "slavery" was Jim Crow segregation. Jim Crow (view timeline) Thomas Dartmouth Rice, a struggling white actor, became famous by performing in blackface makeup as "Jim Crow," an exaggerated, highly stereotypical black character. By 1838, the term "Jim Crow" was being used as a collective racial epithet for blacks, not as offensive as nigger, but as offensive as coon or darkie. The popularity of minstrel shows aided the spread of Jim Crow as a racial slur. By the end of the 19th century, Jim Crow was being used to describe laws and customs that oppressed blacks. Civil Rights (view timeline) In the 19th and 20th centuries, the resistance of African Americans to their oppression was expressed in three general approaches, as illustrated by prominent leaders. Booker T. Washington (1856-1915) stressed industrial schooling for African Americans and gradual social adjustment rather than political and civil rights. Marcus Garvey (1887-1940) called for racial separatism and a "Back-to-Africa" colonization program. W.E.B. Du Bois (1868-1963) argued that African Americans were in the United States to stay and should fight for their freedom and political equality; it was this approach that laid the foundation for the American civil rights movement. Post Civil Rights (view timeline) African Americans did not emerge from the civil rights movement fully integrated into American society; this is evident by the disproportionately large numbers of blacks who are in poverty, under-educated, and incarcerated. Nevertheless, the civil rights movement did force the end of legal segregation, and spur the creation of a sizeable black middle class. In the 21st century, race relations remain a contentious issue in many sections of society.

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Electing a President 1. What do you see in the cartoon? 2. What does the layout of the maze convey about our electoral process? 3. What do you think this cartoon suggests? 4. Do you agree with the point that the cartoonist is making? Why or why not? If not, how might you revise the cartoon to reflect your perspective? 1. Stage a debate around the constitutional requirements for the presidency— natural-born citizen, age 35, and 14 years residency. Are these requirements adequate? If not, what requirements do students propose? Consider using the National Constitution Center’s “Town Hall Wall” asking “Should we amend the Constitution to let foreign-born U.S. citizens become president?” to inspire a conversation. 2. Assemble a constitutional convention to discuss reforming the Electoral College. Note that C-SPAN offers free electoral vote maps to classrooms, along with lesson plans, on their website. 3. Students might research current Electoral College reform proposals in Congress. If your state’s senators or representatives have sponsored or supported a proposal, consider inviting that person to your classroom. 4. Find your state’s Certificates of Vote from the 2008 election online from the National Archives. Ask students to analyze the documents, and discuss what role they play in the electoral process. The National Archives also offers a document analysis worksheet. 5. Determine when and where your state’s electors are meeting to certify their votes following the 2012 election. Find out if the proceedings are open to the public or televised. Consider inviting an elector to your classroom to discuss the voting process with students. Ask students to research whether or not your state is part of, or debating participation in, the National Popular Vote Interstate Compact. If your state legislature is debating participation, students might write letters to representatives sharing their thoughts on the issue.

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Bullying, harassment, discrimination and violence all create or contribute to negative social environments. All school communities should have clear definitions outlined in their school policies and procedures for bullying, harassment, discrimination and violence. The following definitions contain the key characteristics and have been taken from the Safe Schools Hub . Bullying (click to expand) Bullying is an ongoing misuse of power in relationships through repeated verbal, physical and/or social behaviour that causes physical and/or psychological harm. It can involve an individual or a group misusing their power over one or more persons. Bullying can happen in person or online, and it can be obvious (overt) or hidden (covert). Bullying of any form or for any reason can have long-term effects on those involved, including bystanders. Single incidents and conflict or fights between equals, whether in person or online, are not defined as bullying. However, these conflicts still need to be addressed and resolved. Behaviours that do not constitute bullying include: - mutual arguments and disagreements (where there is no power imbalance) - not liking someone or a single act of social rejection - one-off acts of meanness or spite - isolated incidents of aggression, intimidation or violence. Online bullying (sometimes referred to as cyberbullying) is bullying carried out through the internet or mobile devices. Not all online issues are bullying. Learn more about cybersafety issues, including online bullying. A student who bullies others may: (click to expand) - send insulting or threatening text messages - post someone's personal or embarrassing information online - create hate sites or start social exclusion campaigns on social networking sites. Harassment (click to expand) Harassment is behaviour that targets an individual or group due to their: - identity, race, culture or ethnic origin - physical characteristics - sexual orientation - marital, parenting or economic status - ability or disability. It offends, humiliates, intimidates or creates a hostile environment. It may be: - an ongoing pattern of behaviour or a single act - directed randomly or towards the same person(s) - intentional or unintentional. Examples of harassment: (click to expand) Some examples of harassment include where students: - ridicule someone who doesn't speak English - tease someone who wears different clothes due to religion/beliefs - make suggestive comments or insults based on sex - make fun of someone who needs a wheelchair or walking frame for mobility - put down someone who is obese or very thin - tell offensive jokes deliberately to put down a particular societal group. Discrimination (click to expand) Examples of discrimination: (click to expand) Some examples of discrimination include where students: - exclude children of a different culture from a friendship group - don't let children of a different race sit near them at lunch - refuse to include a student with a disability in their game. Discrimination interferes with the legal right of all people to be treated fairly and have the same opportunities as everyone else. Violence (click to expand) Violence is the intentional use of physical force or power, threatened or actual, against another person(s) that results in psychological harm, injury or in some cases death. It may involve provoked or unprovoked acts and can be a single incident, a random act or can occur over time. Types of violence: (click to expand) Violence can fall into three basic categories: - self-directed violence (e.g. self abuse and suicide) - collective violence (e.g. social and political violence including war and terrorism) - interpersonal violence (e.g. family and intimate partner violence, community violence involving an acquaintance or stranger). Some examples of violence a teacher may observe include: - throwing items - hitting with fists - using a sharp instrument - hitting with an object - pulling hair. It is important to remember that bullying and violence are not the same issue. Violence is often an outcome and is certainly an arm of bullying. If bullying can be addressed in its earlier stages then many instances of violence could be prevented. It is important that bullying and violence are treated as separate issues with their own responses, but both issues are as important as each other and both can have a devastating effect on young people.

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On the West Coast, California was less impacted by Black migration from the South. California's Black population numbered around 21,645 in 1910, making this primarily urban population less than one percent of California's entire population. Yet California's Black community had successfully come together to gain civil rights for Blacks through high-profile court cases starting in the 1860s.In the 1890s, Black activist organizations such as the Afro-American League and the National Association for the Advancement of Colored People linked California Blacks to the statewide and nationwide struggle for Black rights. Economically, however, Black Californians were still restricted. While there was no legal segregation, Blacks in California in 1910 were still limited to the same occupations of the previous century: domestic workers and manual laborers. Successful Black professionals, entrepreneurs, and even Black millionaires certainly existed but were the exception, not the rule. The large-scale recruiting of Blacks to work in World War I war industries was the first sign that changes to the economic situation of Blacks in California might be possible. In Los Angeles in 1918, the Black community, which expanded shortly before World War I to become larger than those of Oakland and San Francisco, elected the first Black assemblyman to the California State Congress. Black men and women had access to higher-paying skilled wartime jobs, and urban Black communities in major California cities expanded. However, with the end of World War I came the end of war industry jobs. The U.S. may have celebrated the victorious conclusion of the war, but Black communities in California were hard-hit. True changes in employment opportunities for Blacks would have to wait. 11.5 Students analyze the major political, social, economic, technological, and cultural developments of the 1920s. (11.5.2, 11.5.5)

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1 The Real Numbers1.1 The Set of Real Numbers1.2 Operations and Properties 1.3 Inequalities and Absolute Values1.4 Algebraic Expressions1.5 Properties of Exponents and Scientific Notation2 Linear Equations and Inequalities2.1 Solutions of Linear Equations in One Variable2.2 Literal Equations and Formulas2.3 Applications and Problem Solving2.4 Linear Inequalities2.5 Absolute Value Equations and Inequalities3 Graphs of Linear Relations and Functions3.1 Graphing Linear Equations3.2 An Introduction to Functions3.3 The Slope of a Line3.4 Forms of Linear Equations3.5 Graphing Absolute Value Functions and Linear Inequalities 4 Systems of Linear Relations4.1 Systems of Linear Equations in Two Variables 4.2 Systems of Linear Equations in Three Variables 4.3 Solving Systems of Equations Using Matrices4.4 Graphing Systems of Linear Inequalities5 Polynomials and Polynomial Functions5.1 Addition and Subtraction of Polynomials5.2 Multiplication of Polynomials5.3 Division of Polynomials5.4 Common Factors and Factoring by Grouping 5.5 Factoring Special Binomials5.6 Factoring Trinomials: Trial and Error 5.7 Factoring Trinomials: The ac Method5.8 Strategies in Factoring5.9 Solving Quadratic Equations by Factoring6 Rational Expressions and Functions6.1 Simplification of Rational Expressions and Functions6.2 Multiplication and Division of Rational Expressions6.3 Addition and Subtraction of Rational Expressions 6.4 Complex Fractions6.5 Solving Rational Equations6.6 Variation 7 Radical and Radical Exponents7.1 Roots and Radicals7.2 Simplification of Radical Expressions7.3 Operations on Radical Expressions7.4 Solving Radical Equations7.5 Geometric and Other Applications7.6 Rational Exponents7.7 Complex Numbers8 Quadratic Equations, Functions, and Inequalities8.1 Graphing Factorable Quadratic Functions8.2 Solving Quadratic Equations by Completing the Square8.3 Solving Quadratic Equations by Using the Quadratic Formula8.4 Solving Equations that are Quadratic in Form8.5 Quadratic Inequalities and Rational Inequalities9 Conic Sections9.1 Parabolas9.2 Circles9.3 Ellipses and Hyperbolas9.4 Nonlinear Systems10 Additional Properties of Functions 10.1 Algebra of Functions10.2 Composition of Functions10.3 Inverse Relations and Functions11 Exponential and Logarithmic Functions11.1 Exponential Functions11.2 Logarithmic Functions11.3 Properties of Logarithms11.4 Solving Logarithmic and Exponential EquationsAppendix: Determinants and Cramer’s Rule Back to top Rent Intermediate Algebra 1st edition today, or search our site for Donald textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by McGraw-Hill Science/Engineering/Math.

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Finding rational solutions to linear equations is easy because every nonzero rational number has a multiplicative inverse. Finding integer solutions to linear equations is a bit more complicated because the only integers which have integer multiplicative inverses are ±1. A pleasant surprise is that when working modulo n, one frequently finds that many elements have multiplicative inverses. In this context, the multiplicative inverse (or just "inverse" for short) of a modulo n, which is denoted by a1, satisfies a · a1 1 (mod n). For example, if a = 29, then a1 35 (mod 78). We'll get to how to compute the inverse later in the chapter. For now, we can verify the claim with the following computation: One complication is that not all choices for a will have an inverse mod n. One way to determine if a has an inverse mod n is to simply multiply a by each of 0, 1, 2, . . . , n 1, and then look to see if any of the products is congruent to 1 (mod n). For example, here's what we get for a = 29 and n = 78: As we can see, the output list contains a 1, which indicates that 29 has an inverse mod 78. Moreover, since the 1 appears in the 36th entry, this tells us that 29 · 35 1 (mod 78), as above. On the other hand, here's what we get for a = 32 and n = 78: There's no 1 in the list, so 32 does not have an inverse mod 78. In the first research question, we address the question of which integers a have a multiplicative inverse modulo n. Using the preceding applet to experiment would be tedious. To make matters easier, the applet below will take an integer n as input, and will produce two lists of numbers: those values of a between 0 and n 1 that have inverses, and those values of a between 0 and n 1 that do not have inverses. For example, here's what we get for n = 10: Test out different values of n, and try to determine which values of a will appear for a given value of n. Research Question 1 If n > 0, what values of a (between 0 and n 1) will have an inverse mod n ? Note: You may find it easier to think of this question in the following equivalent form: for which values of a does the congruence equation ax 1 (mod n) have solutions? As you can see, the problem of finding an inverse for a modulo n is really a special case of the general problem considered in the Prelab discussion, namely, to solve the linear congruence equation ax b (mod n). We take up this problem in the next section. Section 5.1 | Section 5.2 | Section 5.3 | Section 5.4 | Section 5.5 | Section 5.6 Chapter 5 | DNT Table of Contents Copyright © 2001 by W. H. Freeman and Company

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Teacher resources and professional development across the curriculum Teacher professional development and classroom resources across the curriculum What does "fair" really mean? Does it mean the same thing to everybody? Sociologists have been able to explore these questions using the techniques of game theory. Games can serve as one of the essential tools of the sociologist, much as litmus paper serves as a tool for the chemist or a telescope serves as a tool for the astronomer. First, let's clarify the difference between the terms "rational" and "fair." A rational action, as we have defined it, is one in which a player chooses the strategy with the best chance of producing the most personal benefit, without regard to what happens to the other player. Being fair, on the other hand, takes into account a whole host of other factors, including cultural norms, experience in market transactions, and experience with cooperation. In work done at the turn of the twenty-first century, researchers found that the concept of what is "fair" ranges widely, depending on who's playing. They reached this conclusion after watching how people from 17 different small-scale societies, ranging from hunter-gatherers to nomadic herders to sedentary farmers, played in a variety of cooperative games, such as the Ultimatum Game and the Public Goods Game. In the Public Goods Game, players are asked to contribute some amount of money to a communal pot, which will be subsequently increased, based on how much everyone gives. In the Ultimatum Game, one player is given a sum of money or other valuable resource and is instructed to share it with another player. The first player decides how much to offer and the second player decides whether or not to accept the offer. If the second player rejects the offer, neither player gets any reward, or benefit. Let's examine the Ultimatum Game in a bit more detail. Player 1, the Offerer, can offer any amount that he or she chooses. For the sake of simplicity, let's say that the Offerer can choose to offer a high amount (H) or a low amount (L). If he offers H, then he will be left with L if Player 2 accepts the offer, and vice versa. Player 2, the Receiver, always has the choice of accepting or rejecting the offer. With these simplified assumptions we can create a matrix: It should be evident from this matrix that a rational Receiver will never reject an offer. From the rational Receiver's point of view, receiving L, even if L is of very low value, is better than getting nothing. A rational Offerer will pick the strategy corresponding to the row with the largest minimum payoff. Both rows in this case have the same minimum, 0, so the Offerer should then choose the strategy with the best potential payoff, which will be to Offer Low. In fact, the rational Offerer should offer the smallest amount possible, because the rational Receiver accepts any offer. When actual people play this game, however, the results vary widely and are never in line with the rational model. The study found that average offers across all societies range from 25% of the total to more than 50%. Furthermore, many real players will reject offers, even offers of more than 50%. What is perhaps more illuminating is how offers and acceptances depend on the society in which the players live. Certain groups of people who are very economically independent, at least at the family level, had the lowest average offers. Other groups of people who depend on communal cooperation to gain food, such as in a whale hunt, had mean offers very close to 50%. Still others, in societies in which gift-giving is an act of status, had average offers above 50%. Quite surprisingly, some of these high-offer societies exhibited high rejection rates as well. Why would someone reject an offer? The answer relates to the psychology inherent in reiterative games. The researchers surmised that people reject offers that are too low because if they accepted such offers, they would develop a reputation for accepting low offers and, consequently, no one would give them higher offers in the future. Also, rejecting an offer turns the tables of power in the Receiver's favor. The Receiver can punish the low Offerer, who has much more to lose in a rejection than the Receiver does. From the Receiver's point of view, it might be worth incurring the cost of losing the low offer if it discourages the Offerer from being so stingy with future offers. Why would anyone reject a high offer? In certain cultures, gift giving obligates the receiver to return the favor; receivers who do not wish to be obligated to someone else would then reject any offer that seemed to be too big a burden to pay back. These cultural norms were thought to manifest themselves in how people played the Ultimatum Game, as the participants sought to contextualize their experience of the game. In other words, they often asked themselves, "What does this game remind me of?" and then they adjusted their strategy to align with their perception of the situation. The Public Goods Game and the Ultimatum Game show that what people perceive as being fair depends heavily on their cultural context. In these cases, games served as tools for measuring and quantifying cultural values in the real world. We see that the concept of fairness develops in human societies in relation to their specific needs and values. Game theory can also be used to examine another very human concept, that of language. We will now turn our attention to how ideas from game theory can contribute to the explanation of how language can arise and develop within a group. Next: 9.7 Language

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The Union victory in the Civil War may have given some 4 million slaves their freedom, but African Americans faced a new onslaught of obstacles and injustices during the Reconstruction era (1865-1877). By late 1865, when the 13th Amendment officially outlawed the institution of slavery, the question of freed blacks’ status in the postwar South was still very much unresolved. Under the lenient Reconstruction policies of President Andrew Johnson, white southerners reestablished civil authority in the former Confederate states in 1865 and 1866. They enacted a series of restrictive laws known as “black codes,” which were designed to restrict freed blacks’ activity and ensure their availability as a labor force now that slavery had been abolished. For instance, many states required blacks to sign yearly labor contracts; if they refused, they risked being arrested as vagrants and fined or forced into unpaid labor. Northern outrage over the black codes helped undermine support for Johnson’s policies, and by late 1866 control over Reconstruction had shifted to the more radical wing of the Republican Party in Congress.

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Fraction Segment Strips Fraction Concepts, More Fraction Concepts, Fraction Operations, Decimals and Fractions In previous fraction lessons, we used egg cartons and base ten mats as area concept models for fractions. In this lesson, we use a linear model, represented by segment strips. These are long, narrow strips of paper, which are subdivided into congruent segment lengths. In this lesson, they serve as a means for comparing fractions, given a relative unit, and as a model for combining various fractions. There are six segment strips: The actual strips are about 11" long - these are short versions If we consider the length of the white segment to be one linear unit, we can determine the relative lengths of the other segments: What fractions of a unit do the other segment lengths represent? How are you thinking about them? Let's let one yellow segment be the linear unit. Now, what lengths are represented by the other segments? Let's find the blue segment's length, then you can try the others: Suppose 3 blue segments equal 1 linear unit. Then what is the length of 5 orange segments? Here's one way of figuring it out, maybe you can think of another: What about the other segments? Another way to use the model is to choose a set of segment strips, say 2 blue and 2 orange segments: What length would they represent if the linear unit were: We also explore ideas like - If the segments above represent 3/4 linear unit, what combinations of other colors / fractions equal the same amount? By exploring and discussing ideas like those above, students gain a deep understanding of fraction relationships and meanings. Activities in basic operations with fractions will further build off of this work. Try to your challenge child, or vice-versa with some situations to explore with the segment strips. (Your child has some!)

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What is a sediment trap and why do we use it? Sediment traps are containers that scientists place in the water to collect particles falling toward the sea floor. The traps collect tiny sediment or larger accumulations called marine snow - made up of organic matter, dead sea creatures, tiny shells, dust and minerals. Analyzing the samples helps scientists understand how fast nutrients and trace elements like carbon, nitrogen, phosphorus, calcium, silicon and uranium move from the ocean surface to the deep ocean. These materials are what almost all deep-sea life uses for food (since plants can’t grow in the dark). Other researchers analyze the trace elements for clues about ocean circulation thousands of years ago. And sediment trap data helps to understand the other end of the nutrient cycle: how upwelling currents create such productive fishing areas. How do sediment traps work? The basic sediment trap consists of a broad funnel with a collecting jar at the bottom. The funnel opening covers a standard area (such as 0.25 square meter [2.7 square feet]) and has baffles at the top to keep out very large objects that might clog the funnel. The trap clamps at a specific depth to a fixed cable attached to an anchor or buoy. Traps are often placed very deep, where they can catch sediment near the ocean bottom. When a ship returns to retrieve the trap, the crew activates a remote-controlled device called an acoustic release. The release severs the line between the trap and its anchor, and the trap floats to the surface with its samples. The first sediment trap was deployed in 1978 off Bermuda, in more than 3,200 meters (2 miles) of water. In more recent experiments, several traps have been spaced every 500 meters from the upper ocean to 500 meters above the seafloor. By comparing the trap catches, scientists learn how much material gets recycled by sea life on its journey downward. How have sediment traps been refined since 1978? automated traps carry up to 21 collection vials on a motorized tray. The pre-programmed unit swaps out the vials at set intervals or when sensors on the unit record a change in water conditions. Each sealed vial stores information about a narrow slice of time, and together they allow the unit to operate continuously for up to a year. Scientists studying the upper ocean use smaller traps that are easier to handle and collect multiple samples at the same time. In shallower waters, much more sediment falls through the water than at depth. That means upper-ocean sediment traps can forgo the bulky funnel top. They can be deployed for only a few days at a time and still collect useful samples. But currents near the surface can be strong enough to push sediment past a trap the way rain can blow past a rain gauge. So scientists designed the neutrally buoyant sediment trap, which drifts with prevailing currents at a specified depth while catching falling sediment. What have we learned using sediment traps? Before sediment traps, scientists assumed that nutrients and the tiny bodies of plankton would sink very slowly, taking centuries or millennia to finally reach the sea floor. During the long descent, they reasoned, much of the material would re-dissolve or be consumed by sea life and never reach bottom. Just how deep-sea life could survive with so few nutrients arriving became a puzzle. Sediment traps showed much larger particles (to 12 mm [0.5 inch] long) than scientists expected. This marine snow sinks as fast as 200 meters (656 feet) per day and can reach bottom in just a few weeks. At that speed, transient surface conditions, like a summer bloom of phytoplankton, can be felt on the sea floor in the form of a blizzard of marine snow. Years of trap data now indicate that about 740 million metric tons (815 million tons) of carbon reaches the global sea floor every year. That’s about 1 percent of the ocean’s total production of carbon in a year. Scientists have made similar calculations for other important elements and nutrients. What platforms are involved? Sediment traps are usually mounted on the mooring cable of a subsurface or a surface buoy. The traps are bolted onto the lines at specific depths, where they remain for up to a year before a research vessel returns to collect the samples. Sediment traps are the only means for scientists to get hard data about the amounts and kinds of material that surface waters transport to the deep ocean. Sturdy titanium construction means traps can be redeployed as soon as the collection vials are replaced. Sediment traps have to remain vertical in the water to work properly. Traps deployed in strong currents must continuously record their tilt angle so scientists can tell whether the samples have been compromised. In deep water, it takes a long time to collect enough sediment for a sample - especially because, back on shore, scientists from a wide range of disciplines are waiting for a part of the sample. The samples can bias themselves. The deep ocean is low on food, so a collection jar filled with sediment is a buffet for local zooplankton. In some traps, the majority of the catch can come from “swimmers” who arrive looking for a meal, and not from sediment at all. Trap designers are working on ways to keep live organisms out of the samples. Susumu Honjo, Scientist Emeritus, Geology and Geophysics, Woods Hole Oceanographic Institution. Steve Manganini, Research Specialist, Geology and Geophysics, Woods Hole Oceanographic Institution. Ken Buesseler, Senior Scientist, Marine Chemistry and Geochemistry, Woods Hole Oceanographic Institution. Buesseler lab website ("Cafe Thorium"). Jim Valdes, Senior Engineer, Physical Oceanography, Woods Hole Oceanographic Institution. Coale, K. H. Labyrinth of doom: a device to minimize the "swimmer" component in sediment trap collections. Limnology and Oceanography 35:1376-1381. (1990) Honjo, S. Trapped particulate flux. p. 3045-3048 in J. H. Steele, K. K. Turekian and S. A. Thorpe (eds.), Encyclopedia of Ocean Science, Academic Press, San Diego, CA. (2001) Lampitt, R. S. Marine snow. p. 1667-1675 in J. H. Steele, K. K. Turekian and S. A. Thorpe (eds.), Encyclopedia of Ocean Science, Academic Press, San Diego, CA. (2001) Valdes, J. R., and J. F. Price. A neutrally buoyant, upper ocean sediment trap. Journal of Atmospheric and Oceanic Technology 17:62-68 [doi:10.1175/1520-0426(2000)017<0062:ANBUOS>2.0.CO;2]. (1999) Last updated: February 24, 2007

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Satellite radar data showed two wave fronts combining into a doubly tall tsunami off the coast of Japan on March 11. The tsunami that spawned by the 9.0 earthquake off Japan this March was a disaster of massive proportions, reaching heights of over 130 feet in some areas and traveling up to six miles inland in others. Scientists at NASA and Ohio State University have now found another factor, beyond the sheer strength of the quake, that made the tsunami so ferocious: It started out as two separate walls of waves that combined to form one taller, more powerful “merging tsunami.” Three different satellites happened to fly over the tsunami on March 11. Using their onboard radar altimeters, the satellites could gauge sea level changes within inches, producing a detailed picture of how the tsunami developed—and why it was so destructive when it hit land. As NASA explains: Data from NASA and European radar satellites captured at least two wave fronts that day. The fronts merged to form a single, double-high wave far out at sea. This wave was capable of traveling long distances without losing power. Ocean ridges and undersea mountain chains pushed the waves together along certain directions from the tsunami’s origin. While scientists have long suspected that such merging tsunamis exist, this is the first time they’ve been able to observe one. Understanding how and where these extra-strength tsunamis form, the researchers say, could help them build more accurate hazard maps for coastal areas. Image courtesy of NASA/JPL-Caltech/Ohio State University

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CBSE Maths eBooks Chapter 17: Co-ordinate Geometry We are already familiar with plotting a point on a plane graph paper. For this we take two perpendicular lines XoX’ and YoY’ intersecting at O. XOX’ is called x-axis or abscissa and YoY’ is called y-axis or ordinate. Point in a plane Let us take a point P in a plane. Let XOX’ and YOY’ be pendicualr to each other at O. are drawn. If OM = x and ON = y then x-coordinate of P is x and y-coordinate of P is y. Here we write x-coordinate first. Hence (x, y) and (y, x) are different point whenever . The two lines XOX’ and YOY’ divides the plane into four parts called quadrants. XOY, YOX’, X’OY’ and Y’OX are respectively the first second, third and and fourth quadrants. We take the direction from O to X and O to Y as positive and the direction from O to X’ and O to Y’ as negative. Distance between two points Let P (x1, y1) and Q (x2, y2) be the two points. We have to find PQ. Let P (x, y) divided a line AB such that AP : PB = m1 : m2. Let coordinates of A are (x1, y1) and B are (x2, y2).

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PV = nRT is an equation, and it can be manipulated just like all other equations. With this in mind, let's see how the ideal gas law can help us calculate gas density. Density d has the units of mass over volume. The ideal gas law transforms into a form with units in mol per unit volume: |d = =| Dalton's law states that the total pressure of a mixture of gases is the sum of the pressures each constituent gas would exert if it were alone. Dalton's law can be expressed mathematically: |P tot = P A + P B + P C + ...| Each individual gas obeys the ideal gas law, so we can rearrange PV = nRT to find pressure: |P A = n a| Dalton's law problems often present two containers of gas, mix them, and ask you to find the partial pressures of each gas. There's usually an easy way and a hard way to do such problems; the trick is finding the easy way. You'll gain this intuition quickest if you jump right in. Try your hand at the problems at the end of this section and in your textbook.

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Like these materials? Show your support by liking us on Facebook... In grammar, a part of speech is a linguistic category of words, which is generally defined by the syntactic or morphological behavior of the lexical item in question. Common linguistic categories include noun and verb, among others. There are open word classes, which constantly acquire new members, and closed word classes, which acquire new members infrequently if at all. Almost all languages have the lexical categories noun and verb, but beyond these there are significant variations in different languages. For example, Japanese has as many as three classes of adjectives where English has one; Chinese, Korean and Japanese have nominal classifiers whereas European languages do not; many languages do not have a distinction between adjectives and adverbs, adjectives and verbs or adjectives and nouns, etc. This variation in the number of categories and their identifying properties entails that analysis be done for each individual language. Nevertheless the labels for each category are assigned on the basis of universal criteria. Below you'll find printable parts of speech worksheets. On these worksheets, students learn to identify the part of speech of a word according to how it is used in a given sentence. Then, they are given opportunity to practice writing sentences using the specified part of speech. All eight parts of speech are covered in this section: Nouns, Verbs, Adjectives, Adverbs, Prepositions, Interjections, Pronouns, and Conjunctions. Below you will find our full list of printable prepositions worksheets to be used by teachers at home or in school. Just click on a link to open a printable PDF version of the desired worksheet. We hope you find them useful. Explanation, examples, and practice identifying prepositions in sentences. Answers to the Identifying Prepositions worksheet. This worksheet includes a table outlining the various prepositions of time and their usages. Practice involves using prepositions of time to explain the schedules of color characters in the worksheet. Answers to the Prepositions of Time Worksheet. The worksheet provides practice using images to explain the positions of people and objects in relation to one another. Answers to the Prepositions of Place Worksheet 1 The worksheet includes tables outlining the various prepositions of place (location). Practice involves using prepositions of place to explain the positions of color objects in relation to one another. Answers to the Prepositions of Place Worksheet 2 This section contains printable worksheets on nouns.

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To prepare, gather materials for the Day 2 lab. As a warm-up, have students take out their periodic tables and answer the following questions in their notes (S-C-8_Periodic Table.pdf): 1. What is the atomic mass of carbon? (12.01) 2. What does atomic mass measure? (the mass of an atom of an element) 3. What is the unit for atomic mass? (atomic mass units (amu)) Go over the answers to the warm-up activity. As an introduction to the mole, show students slides 1–18 on the slideshow at How Big Is a Mole available from www.slideshare.net/vmizner/how-big-is-a-mole. Afterward, show students the Just How Big Is a Mole? resource (S-C-8-1_Just How Big Is a Mole.doc). Ask them to explain why a mole of popcorn seeds is larger than a mole of salt grains. Also, have them use Avogadro’s number to describe a mole of popcorn seeds and a mole of salt grains. Show students The Mole PowerPoint Presentation (S-C-8-1_The Mole PowerPoint Presentation.pptx). Have students take notes during the PowerPoint presentation. Also, have them solve the practice problems in their notes before you reveal and explain the answers. Provide additional practice by having students solve the following conversion problem. How many atoms are in 2.5 moles of titanium? moles × atoms/mole = atoms of Ti 2.5 moles × 6.02 x 1023 atoms/1 mole = 1.5 x 1024 atoms of Ti Have a volunteer write the units only for the solution on the board, leaving room to add the numbers. Once the units are in place, have another student add the numbers. Then, solve the problem together as a class. Check that students understand how to set up conversion equations. Provide additional practice if needed. Hand out copies of Comparing Sugar and Water (S-C-8-1_Comparing Sugar and Water and KEY.doc). Have students work in pairs to complete the table, and then go over the answers with the class. Have students work individually to complete the Mole Concepts worksheet (S-C-8-1_Mole Concepts Worksheet and KEY.doc). For homework, assign the Mass-Mole Conversions worksheet (S-C-8-1_Mass-Mole Conversions Worksheet and KEY.doc). Collect the homework, the Mass-Mole Conversions Worksheet (S-C-8-1_Mass-Mole Conversions Worksheet and KEY.doc). Hand out copies of the Lab: Would a Mole of Pennies Fit Inside our Classroom? (S-C-8-1_A Mole of Pennies Lab and KEY.doc). Explain the objective of the lab. Review the mole concept from Day 1, and discuss conversion factors if needed. Divide students into groups of four and have them complete the lab. Monitor the classroom and assist with calculations if students need support. On an exit slip, ask students to write a sentence explaining how the mole concept is like using dozens or hours as standards. Example response: Chemists use the mole as a shortcut for measuring large amounts of particles, like we use dozens as a shortcut to measure objects or hours to measure time more easily. Optional: Play the song “A Mole Is a Unit,” which can be found on various Web sites including www.youtube.com/watch?v=1R7NiIum2TI, to reinforce the mole concept and conclude the lesson. - To support the solving of mass-mole problems, provide students who might need an opportunity for additional learning with a table of atomic weights that is arranged in alphabetical order, such as the one at: www.medicinescomplete.com/mc/merck/2010/AtomicWeights.pdf. - Students who might need an opportunity for additional learning can prepare index cards with the conversion factors on them to use as they solve problems. Also, you can provide a list of the lesson’s vocabulary. Review other related terms if needed (e.g., atoms, molecules, compounds, and ions). - During the lab, support students by walking them step-by-step through the calculations and explaining the conversion factors. - Challenge students who may be going beyond the standards to solve the following problem: “A mole of pennies stacked end to end would reach from Earth to the Sun and back how many times?” (Almost 500 million times) - As an extension for the lab activity, have students who might be going beyond the standards calculate about how many moles of M&M’s it would take to fill the volume of the Earth’s oceans (i.e., 1.35 ×109 km3)? (It would take about 3 moles of M&M’s®.) See calculations at www.madsci.org/posts/archives/2002-02/1013032438.Ch.r.html.

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Here are five important documents written by free black Northerners in the decades before the Civil War. Together, they help capture the range of concerns captured in the antebellum black protest tradition. This exercise will introduce students to some of the central ideas African-American leaders set forth in their writings. Divide the class into five groups, each of which will be assigned a document. If possible, prepare groups and assign readings before class. Students in each group work together to read through the document and address the five questions listed below. Once groups have had time to discuss their documents, reconvene the class. Each group may then present its document to the class. Time permitting, the class may then consider the larger questions for consideration listed below. A Free Woman of Color Lectures on Prejudice and Morality, 1832 2. An African-American Bishop Recalls Conflicts over Styles of Worship, 1888 3. Address of the Colored National Convention to the People of the United States, 1853 4. A Black Nationalist Manifesto, 1854 5. A Call for Morality over Money, 1859 1. Who does the author's audience seem to be? For whom were the words of the document intended? 2. What does the author of the document seem to want? If several things, what seems to be the central thing? Make sure you highlight the parts of the document that suggest the author's central goal. 3. What argument does the author make to go about achieving the goal? 4. Do you think this argument would have worked to convince the author's intended audience? In what ways yes and in what ways no? 5. As a modern reader, what parts of the argument seem persuasive to you and which seem less so? Why? Questions for consideration: 1. What, according to the documents, were the major problems confronting African Americans? 2. What were some of the ways African Americans wanted to change American society? 3. On what kinds of values did they base their appeals? In other words, how did they hope to change the minds of their audiences? 4. In what ways might their arguments still have power today? In what ways might their message fail to connect to people today? Remember that just as they spoke to different audiences in their own day, they would have to speak to a variety of audiences today. 5. Do these documents reveal any differences among African Americans? If so, about what was there tension? How might these tensions have led to differing ideas on how best to achieve equality?

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Click here for a printable version Title: Mineral Identification Core Content for Assessment: The purpose of this activity is to teach the student to identify minerals from its physical properties. This is accomplished through observation and testing of the minerals involved. Set up mineral stations for each mineral the students are to identify. If necessary, some stations may have two minerals to identify. Each station should be equipped with one each of the following items: Divide students into equal groups. Have the number of student groups match the number of mineral stations. Distribute to each student a Mineral Worksheet and Mineral Background sheet. Have students read the Mineral Background sheet. Have student groups move to the mineral stations with one group of students at each station. Have the students perform the physical property tests listed on the Mineral Background sheet. Have students record the test results on the Mineral Worksheet. Rotate the student groups through each of the work stations, performing the tests at each station. Allow 3 to 5 minutes per mineral per station. Handout Mineral Identification Sheets. Have students compare their test results with the Mineral Identification sheet. Can the students correctly name each of the minerals using their test results? Write the name of the mineral on the Mineral Worksheet. The students learned to perform tests for physical properties of minerals, observe the test results and then identify a mineral using the test results. MINERAL BACKGROUND SHEET The following is a description of the Physical Properties that are used to identify minerals: Feel - Texture of the mineral Hardness - Mohs Scale |Hardness||Mineral scratched by| |5||Steel (knife blade)| |7-10||Mineral will scratch steel/glass| Adapted from materials provided by Women In Mining

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- Describe the complementary relationships between pollinators and the plants they pollinate. - Identify adaptations that flowers have developed to "encourage" pollination. - Copies of Activity Pages 3A and 3B and the Take-Home Page (See Required Materials links for the Activity Sheets) - Pens, pencils, crayons. - Science, language arts, art 1. Begin the lesson by explaining that over time flowers have developed adaptations to ensure that the best pollinator (one that will carry pollen onto another flower of the same species) will return again and again. Pollinators such as hummingbirds and honeybees have also adapted to ensure that they will have a plentiful food supply. 2. Give each student a copy of Activity Page 3A. Explain that you're trying to determine which animal would make the best pollinator for the trumpet flower. Have your students study the pictures while you provide the following background: - The trumpet flower is red in color, has an upside-down "tube" shape, has no "landing" spot, and has little fragrance. - Hummingbirds have a poorly developed sense of smell; are attracted to the colors red, pink, orange, and yellow; "hover" at, rather than land on, their flowers; and have a long bill and tongue. - Honeybees have a short proboscis, cannot see red, must land and crawl, and are attracted to sweet fragrances. 3. Have your students answer the questions on Activity Page 3A. (Is the honeybee or the hummingbird more likely to access the nectar? Is the shape of this particular flower more appropriate for a honeybee or a hummingbird? Which pollinator would be more attracted to the flower's color? Would a honeybee be lured by the trumpet flower's scent? Is there a place for a honeybee to land? Which animal would make the best pollinator for the trumpet flower?) 4. Give each student a copy of Activity Page 3B Remind them that flowers are designed to attract pollinators with specific tastes and attributes. Have your students answer the following questions on Activity Page 3B: - What is your favorite color? - What is your favorite shape? - What smells good to you? - What is your favorite snack? 5. Have your students pair off. Instruct them to state their preferences, which they've listed on Activity Page 3B. Then have each of them draw simultaneously their partner's "designer flower." For fun, have them make it as unreal as possible. For example, one might design a flower that is black, triangular in shape, smells like fresh-baked brownies, and provides pizza as a reward. Have each pair present their "designer flowers" to the class. As an extension, have the artist be the flower, designing "adaptations" suited to his or her partner's preferences. 6. Direct your students to the Take-Home Page. Tell them to think up and draw a fictional pollinator-plant pair. (For example, a flower that smells like Swiss cheese would likely attract a rodent pollinator.) Remind students that the goal is to get the animal to pick up the pollen and carry it to another plant of the same species. Have them list the attributes of the plant that attract the pollinator and the mechanism or mechanisms by which the pollinator carries the pollen to the next plant.

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This chapter introduces the student to discrete random variables and a basic theoretical probability formula. Also covered are Tree Diagrams and basic methods for using a calculator to determine actual probabilities. This chapter furthers a students understanding of distribution by introducing the normal distribution curve, continuing to explore the bell-curve, and covering the use of a calculator in finding the standard deviation. This chapter expands a student's ability to manage data through the introduction of more diverse and complex graphs. CK-12 Foundation’s Basic Probability and Statistics – A Short Course is an introduction to theoretical probability and data organization. Students learn about events, conditions, random variables, and graphs and tables that allow them to manage data.

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Today's students complete most of their homework on a computer and do the bulk of their research online. When tasked with learning something new, they often equate research with “Googling”; assume that the information they find online is true; and produce cut-and-paste work that reflects little original thinking or regard for accuracy. Because the Internet provides direct access to huge volumes of information, students must learn how to filter and analyze their search results to distinguish reliable content and credible sources from incorrect, incomplete or speculative information. Lesson Description: For this lesson, students will go on a treasure hunt for information on a website dedicated to world explorers, only to discover that the facts provided on the site are wrong. Begin with a group discussion about students' preconceptions of the Internet. Next, explain that they will be studying world explorers, and ask them to Google the phrase “all about explorers” to gather information on the topic. Have students browse the first website in the results list (allaboutexplorers.com), and then ask them to click on the “Treasure Hunts” tab near the top of the page. Divide students into pairs to research one of the 12 explorers listed on the “Treasure Hunts” page. Each pair should research and answer three questions about their explorer using the resources provided. Pairs researching the same explorer should then discuss their findings and answer “The Big Question”: What were the similarities and differences in the information you found on the two sites? Students typically are astounded to discover that there's erroneous information on the Internet – especially when it comes from the first source provided in Google's search results. Follow this revelation with further discussions about where to find trustworthy information and how and why to examine a website before trusting the information found there. Subject Area: This activity focuses on digital literacy and social studies subject matter and can be adapted for all grades. Curriculum Standards: This lesson addresses curriculum standards set forth by the Pennsylvania Department of Education and the International Society for Technology in Education's National Educational Technology Standards for Students. The standards challenge students to: Grading Rubric: Students should be evaluated on their:

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As greenhouse gas emissions continue to rise, researchers are looking at a source of even more carbon emissions: thawing permafrost. A warming Arctic may cause significant amounts of dead, organic material currently frozen in permafrost to thaw out and decay, releasing more carbon into the atmosphere. How exactly does permafrost store carbon? And what are the consequences if the permafrost thaws? Carbon and permafrost Permafrost is soil with temperatures at or below 0 degrees Celsius for at least two or more years in a row. Some areas of permafrost absorb enough heat in the summer time to let the topmost layer of soil, called the active layer, to temporarily thaw, allowing plants to grow and animals to find food. Underneath this layer, the soil remains frozen, preventing decay and preserving plant matter and organic material for thousands of years. If temperatures rise and permafrost thaws, the organic material decays, and the soil becomes wet and marshy. As the organic material rots, most of the carbon is released into the atmosphere as carbon dioxide, but in this moist environment, a significant fraction of the carbon is released as methane, a potent greenhouse gas. When the frozen ground thaws, the soil may also collapse and creates holes in the tundra, exposing the old carbon directly to the atmosphere and accelerating its decay. On a local scale, permafrost thaw has direct and immediate impacts for people and animals living in the Arctic. As the ice in the permafrost melts, the ground becomes unstable. Houses and buildings that previously rested on solid frozen soil sink and structural foundations crack. Thawing permafrost also causes roads to heave and crack, making travel difficult. When temperatures rise and the active layer becomes thicker, the Arctic is also likely to become greener as more plants are able to survive the terrain and climate. Arctic tundra vegetation and needle-leaf forests are advancing northward, as deciduous shrubs and other nonnative vegetation edge to higher latitudes. The encroaching shrubs replace the tundra vegetation, which feeds caribou, hares, and marmots. In turn, these animals are vital food sources for Arctic predators. Thawing permafrost may lead to a decline in biodiversity for both vegetation and wildlife. While local effects of thawing permafrost are worrisome, the sheer amount of carbon that could be released in the future concerns everyone. Scientists estimate that Arctic permafrost contains nearly 1,700 billion tons of carbon, about twice the carbon currently in the atmosphere. Methane is over twenty-five times more potent at retaining heat than its carbon dioxide counterpart. In addition, carbon dioxide released due to thawing permafrost is a phenomenon only recently discovered and could convert Arctic carbon into carbon dioxide much more quickly than previously thought. As the Arctic continues to thaw, scientists continue to study its impact on local and global systems, as well as raise awareness about increased greenhouse gas emissions in the atmosphere. The carbon released into the atmosphere from permafrost, either as methane or carbon dioxide, accelerates the increase global temperatures, which may thaw more frozen ground. At this rate, permafrost may be not only a consequence of global climate change, but a contributor to it as well. Cory, R. M., R. C. Crump, J. A. Dobkowski, and G. W. Kling. 2013. Surface exposure to sunlight stimulates CO2 release from permafrost soil carbon in the Arctic. Proceedings of the National Academy of Sciences of the United States of America 110(9), doi:10.1073/pnas.1214104110. Schaefer, K., T. Zhang, L. Bruhwiler, and A. P. Barrett. 2011. Amount and timing of permafrost carbon release in response to climate warming. Tellus 63B: 165-180. Links to previous Icelights posts and sources for more information

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A single point where the entire weight or mass of a body is concentrated is known as center of gravity of that body. Center of gravity is generally denoted by “G”. Centroid is another related term to center of gravity. It is the centroid of plane geometrical figures like rectangle, triangle, trapezoid, circle, etc… word Centroid is used when there is only geometrical figures instead of weight or mass. Therefore, center of gravity of plane geometrical figures is termed as centroid or center of that area. Two distances are required for each area in evaluation of center of gravity. One is from reference X-axis and the other is from reference Y-axis. These two distances are known as centeroidal distances. Centeroidal distances are represented by a bar over the coordinate axis. The X-bar () indicates the X-coordinate of the centroid which is measured in the X-axis direction from reference Y-axis. On the other hand Y-bar () indicates the Y-coordinate of the centroid of area which is measured in the Y-axis direction from reference X-axis. As shown in the figure below. centroid or Center of gravity can be determined by any of the following four methods. These methods are: - By Geometrical Consideration - By Method of Moments - By Graphical Method - By Integration Method

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Common Core Standards: Math Ratios and Proportional Relationships 6.RP.A.1 1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes." For many students, identifying and maintaining a ratio can be challenging until you make the context personal and, you know, not boring. Sure, Susie might have 3 red apples for every green apple, but students will be much more interested to know she also has 2 red dragons for every 3 green dragons. Dragons need to eat healthy, too, you know. Students should understand that a ratio is a comparison of basically anything. They should be able to sort ratios into one of three types: - Part-to-part (using the same unit of measure): For every two red dragons, there are three green dragons. - Part-to-whole (using the same unit of measure): Out of five dragons, two of them are red. - Rates (using different units of measure): A dragon eats fifteen apples for every minute. Under this standard, students are expected to identify rates, but not much else. For more on those bad boys, check out 6.RP.2. We can write out ratios numerically in three different ways: using a colon, the word "to," or a fraction bar. The ratio of two to three can be written as 2:3, 2 to 3, or ⅔. (It's important to stress that only part-to-whole ratios are true fractions. The other ones want to trick us, but come on. Those Groucho glasses aren't fooling anyone.) Students should be comfortable multiplying fractions and generating equivalent ones. This will help them see the relationship between two quantities in a ratio. If students are having trouble figuring out which number goes where or what it all means, it might be time to whip out the sketchpad and express these ratios visually. Encourage students to label the parts and the whole so that their descriptions stay consistent. Green dragons should always be referred to as green dragons, not suddenly basilisks or dinosaurs. Students might have trouble with the mystical "third" numerical value: the whole. We have two red dragons and three green dragons, but it's the drawing that unveils there are five total dragons. And they're all guarding treasure of unfathomable wealth. With a bit of practice, they'll begin to see and understand the multiplicative relationship between equivalent ratios as ratios grow (increase in magnitude) and shrink (toward their simplest form). Students are basically discovering proportional relationships, but they won't actually find missing values with proportions until later, so avoid the "cross-multiply and divide" approach when growing and shrinking ratios. For this standard, language is the key to describing proportional relationships. Think of it like a game of Mad Libs where the templates are: - For every __________ there are ____________. - There ___________ for every _____________. - The ratio of __________ to ____________ is ___ to ____. If students are really struggling to translate between words and numbers, have them explain what the words mean, and then sketch out the relationship labeling the two parts and the whole. If they're having trouble going from numbers to words, suggest writing out some ratio Mad Libs before filling in the blanks. This is all super important because it gets students ready for concepts like percent and slope. It's also a great opportunity to promote an introduction to 6.NS.8, where students review constructing a table and graphing ordered pairs to visually express a ratio's linear relationship.

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The doppler plot below presents the velocity change of the Mars Climate Orbiter spacecraft. This velocity change is measured as a "Doppler shift." The Doppler shift of a radio signal sent by the spacecraft is proportional to the line-of-sight (direction from the Earth to the spacecraft) or Earthline velocity of the spacecraft. The Doppler shift is a frequency shift measured in Hertz (Hz). The gravity of Mars changes the velocity (magnitude and direction) of the spacecraft, and this change in velocity shows up as a Doppler shift of the radio signal sent from the spacecraft. Most people are familiar with the phenomenon of a car horn or train whistle changing its frequency as it moves towards or away from them. Electromagnetic radiation (e.g. light waves or radio signals) also experience this effect. The size of the frequency shift, or "Doppler shift," depends on how fast the light source is moving relative to the observer. Astronomers often refer to the "redshift" and "blueshift" of visible light, where the light from an object coming towards us is shifted to the blue end of the spectrum (higher frequencies), and light from an object moving away is shifted towards the red (lower frequencies). Mars Climate Orbiter commmunicates with controllers on the ground by radio signal. Ground controllers know the frequency of the signal that is transmitted from the spacecraft. However, since the spacecraft is always moving away from or towards us, the transimitted signal is being Doppler shifted to a different frequency. Engineers then compute the Doppler shift by comparing the frequency received on the ground to the known transmitted frequency. It is then straightforward to find the velocity change that would cause the resulting Doppler shift. (Note that this gives us only the line-of-sight velocity.) Again, the frequency shift is measured in Hertz (Hz). |Home||Mars Climate Orbiter||Mars Polar Lander||Deep Space 2 Microprobes| For questions or comments on this website please refer to our list of contacts.

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Your children have encountered patterns without knowing what they were. Introduce patterns by playing a game that has children become part of the pattern. Prerequisite Skills and Concepts: Children should have an understanding of same and different. They should be able to name colors and shapes, and differentiate sizes. Have 8 or 10 children come to the front of the room. Have every other child stand while the rest of the children sit. - Ask: Can you tell me anything about what you see? Children should say that some children are sitting and some children are standing. - Ask: If another child joined the children, would that child sit or stand? Depending on what position the last child is in, the next child will either sit or stand. - Continue adding children to the line, while children at their seats predict the next position. - Ask: What do you see happening here? Elicit from children that the positions of the children are repeated. - Say: Something that repeats over and over in the same order is called a pattern. We are going to learn how to recognize patterns and how to copy and extend them. - Continue having children do patterns throughout the day as they line up or during free time. You may do motions such as, hands up over the head, hands at their sides, or stand, sit, squat, and so on. Try introducing AAB, ABB, and ABC patterns as children become comfortable with the concept of patterning. (An AAB pattern could be sit, sit, stand; an ABB pattern sit, stand, stand; an ABC pattern sit, stand, squat.) These body patterns will prepare them for making patterns with materials. At some point, you may want to have a child get into an incorrect position for a pattern to see if children notice that it is wrong and if they can suggest a way to correct it.

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reading this section you will be able to do how current can be induced in a conductor without making contact. the process of induction. We have now seen that if electrical current is flowing in a conductor, there is an associated magnetic field created around the wire. In a similar manner, if we move a wire inside a magnetic field there will be an electrical current that will be generated in the wire. Current is produced in a conductor when it is moved through a magnetic field because the magnetic lines of force are applying a force on the free electrons in the conductor and causing them to move. This process of generating current in a conductor by placing the conductor in a changing magnetic field is called induction. This is called induction because there is no physical connection between the conductor and the magnet. The current is said to be induced in the conductor by the magnetic field. One requirement for this electromagnetic induction to take place is that the conductor, which is often a piece of wire, must be perpendicular to the magnetic lines of force in order to produce the maximum force on the free electrons. The direction that the induced current flows is determined by the direction of the lines of force and by the direction the wire is moving in the field. In the animation above the ammeter (the instrument used to measure current) indicates when there is current in the conductor. If an AC current is fed through a piece of wire, the electromagnetic field that is produced is constantly growing and shrinking due to the constantly changing current in the wire. This growing and shrinking magnetic field can induce electrical current in another wire that is held close to the first wire. The current in the second wire will also be AC and in fact will look very similar to the current flowing in the first wire. It is common to wrap the wire into a coil to concentrate the strength of the magnetic field at the ends of the coil. Wrapping the coil around an iron bar will further concentrate the magnetic field in the iron bar. The magnetic field will be strongest inside the bar and at its ends (poles).

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Beginning, Middle, and End: Open-ended Story Writing Lesson, PPt with 61 slides and 250 PDF pages, including rubrics FREEBIE IN PREVIEW A foldables printable and a kindergarten printable added. See also the Notebook File version of the same lesson for the SMART Board. See also the PDF version of the same lesson. See also the grade 2 only printable. *NOTE: This is a completely animated Power Point, in view slide show mode. Just keep clicking to see sequences numbered automatically. The PDFs are included in the zip folder. Students and teachers may move the numbers and sequenced activities in the normal mode, also. Interactive Student Notebook pages included Kindergarten section included Beginning, Middle, and End of story writing is something that emergent writers need to practice. (See Common Core standards, below) This Power Point reviews the beginning, middle, and end of some familiar stories. Sequencing of sentences is also covered. Students practice drawing a story using a graphic organizer for the three parts of beginning, middle, and end of their own story. Then, finally, students write their stories from the graphic organizer on three stapled pages (see separate free listing with the printable student pages) with the beginning on page one, the middle part of the story on page two, and the ending on page three. The three part drawing may be referred to as students think about which part of the story belongs on each page. Teachers and peer editors could say, "Tell me about your drawings." Telling about the drawing often prompts students to know what to write. There are several beginning-middle-end work pages to choose from to differentiate this assignment. After students are successful with one, others could be offered. Included are open-ended "chapter books" for students to write. English Language Arts Standards, Writing, Grade 1 Text Types and Purposes 1. Write narratives in which they recount two or more appropriately sequenced events, include some details regarding what happened, use temporal words to signal event order, and provide some sense of closure. COMMON CORE STANDARDS: English Language Arts Standards, Reading: Literature, Grade 2 Craft and Structure 1.Describe the overall structure of a story, including describing how the beginning introduces the story and the ending concludes the action. English Language Arts Standards, Writing, Grade 2 Text Types and Purposes 1.Write narratives in which they recount a well-elaborated event or short sequence of events, include details to describe actions, thoughts, and feelings, use temporal words to signal event order, and provide a sense of closure. Graphics licensed through the Graphics Factory. Carolyn Wilhelm, NBCT Wise Owl Factory

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The Jim Crow Era “Black codes” were passed soon after the Thirteenth Amendment became law in 1866, disallowing blacks the right to testify against whites, to serve on juries, to have full access to the courts, and to vote. Some black codes even required that former slaves sign yearly labor contracts, thus restricting their economic freedom and guaranteeing their subservient position (1). The freedmen were at a legal and economic disadvantage. In Louisiana, a local ordinance required that every African American be in the service of a white person who would be held responsible for his conduct. Blacks were not allowed to join militias or own weapons; insulting acts against whites were punished in some states. “Jim Crow,” which would soon become synonymous with racial segregation, and would become the official policy of the South after Plessy v. Ferguson, was already unofficially preventing African Americans from riding in first-class passenger cars and intruding “into any religious or other assembly of white persons” (2). Schools were always segregated. Some examples of Jim Crow laws from Louisiana, Mississippi, and Virginia are: It's important to note that Jim Crow was a national phenomenon, not caged only in the South. The legalization of Jim Crow did began in the South, but soon spread to all parts of the country, and concerned other ethnicities, not African-Americans. An interesting social history dealing partly with early twentieth-century segregation in Chicago is Arc of Justice, by historian Kevin Boyle. Some examples of Jim Crow laws outside of the South: Although historian C. Vann Woodward posits an interesting argument in his book, The Strange Career of Jim Crow, that racial segregation did not begin until the turn of the nineteenth century, many historians and legal experts disagree with Woodward: “Woodward's critics contended that many aspects of racial segregation, even if not always enshrined in positive law, were put in place shortly after the Civil War if not before” (3). The “black codes” were a response to the Thirteenth Amendment by the Southern democrats, who saw “almost everything the freedpeople” gained as a loss of white political power (4). To respond to the insufficiency and ambiguity of the Thirteenth Amendment, the Northern republicans crafted the Civil Rights Act of 1866 and the Fourteenth Amendment to broaden the definition of citizenship by making it more inclusive, to trump the “black codes,” and to guard the civil rights of the freedmen (5). Both were very controversial and resulted in the impeachment and near conviction of President Johnson. Presidential Reconstruction was at an end; radical Reconstruction, in the hands of fervent republicans, was just beginning (6). Restaurants, fountains, toilets, cemeteries, hospitals, phone booths, public schools, libraries, and parks were quickly being segregated. In North Carolina, white children were forbidden to use schoolbooks that had been touched by blacks. In Alabama, it was criminal for blacks and whites to play checkers together. Lynchings were on the rise. It was as if “Plessy was seen throughout the South as an invitation to treat African Americans virtually as lepers” (7). Anti-miscegenation laws, disfranchisement statutes, and school segregation that were spreading since the end of Reconstruction now received solid backing by Plessy (8). By 1900, Jim Crow was firmly embedded in the South, and spreading. One of the most effective uses of segregation was used in real estate, to guard against blacks moving into white neighborhoods, which ostensibly drove prices down. The job market was affected, as whites became fearful that the blacks, which were migrating northward at a great pace by the turn of the twentieth century, felt the competition. Kevin Boyle vividly discusses the dynamics of Jim Crow in his book Arc of Justice. Housing and jobs inflamed communities across America, and the politics of the era did little to subdue tensions. Official segregation would not end until 1954 with Brown v. Board of Education, which ruled against segregation in the schools. Even after the Fair Housing Act of 1968, blacks are still segregated from whites in certain areas. As Boyle writes, “by then, it was too late. Segregation had become so deeply entrenched in America it couldn't be uprooted, no matter what the law said” (9). “White flight” and “gentrification” are now common concepts in discussing why African Americans, and other minorities, have such a difficult time obtaining desired housing in certain sections of America. 1. Brook Thomas, ed., Plessy v. Ferguson: A Brief History with Documents (Boston: Bedford/St. Martins, 1997), 7. 2. Benjamin Quarles, The Negro in the Making of America, 3rd ed. (New York: Touchstone Book, 1996), 155. 3. Kenneth W. Mack, "Law, Society, Identity, and the Making of the Jim Crow South: Travel and Segregation on Tennessee Railroads, 1875-1905," Law & Social Inquiry 24, no. 2 (Spring, 1999): 378. 4. Suzanne Lebsock, A Murder in Virginia: Southern Justice on Trial (New York: W.W. Norton & Company, 2003), 40. 5. Harvey Fireside, Separate and Unequal: Homer Plessy and the Supreme Court Decision that Legalized Racism (New York: Carroll & Graft Publishers, 2004), 119. 6. Thomas, 8. 7. Fireside, 224. 8. Ronald L. F. Davis, "Creating Jim Crow: In-Depth Essay," n.d., <http://jimcro whistory.org> (retrieved on October 20, 2009). 9. Kevin Boyle, Arc of Justice: A Saga of Race, Civil Rights, and Murder in the Jazz Age (New York: Henry Holt and Company): 89.

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A "route"(when used as a noun), in networking terminology, refers to list of the possible next hops (IP addresses of intermediate routers(layer 3 devices)) which can be taken to reach a particular destination(identified by an IP address). As a verb, "route" is same as "send". Suppose, you want to send IP packets from host1 to host2: So, your "route" or path to host2 from host 1 is: 220.127.116.11>18.104.22.168>22.214.171.124 - From a given source, there can be several "routes" to a destination. This happens because each router decides where to send the packet next(ie, it decides who will be the next hop router). And these next hops form the "route" to the destination. - In Routing Table, a "route" refers to the network. A Routing table basically contains "networks" and the "next hop addresses" for those networks. It also contains other info like cost(used generally when multiple next hops are available for a given network). Answer to Q1: Routes are "written" in the packet forwarding engines(ASICs) of routing devices. It is stored in the form of bits and when a packets comes for routing, the following things happen: a Basic checks of the different checksums and Ethertype are done. b If the DMAC(destination MAC) in the received frame matches the MAC address of the port on which it was received, then the packet is considered for routing. c The forwarding table(it is same as Routing table with only one "next hop" for each "network") is used to decide where to send the packet next. The DIP(destination IP) in the incoming packet is used to perform bit wise AND operation on the "network" entry present in the forwarding table. [For more details, see Answer to Q2] Answer to Q2: A sample Routing table is shown below: IPv4 Route Table Network Destination Netmask Gateway Metric 126.96.36.199 255.255.255.0 188.8.131.52 25 This implies that all packets which have their DIP(destination IP) in the network 184.108.40.206/24, will be forwarded(routed) to the router 220.127.116.11. Suppose an incoming packet arrives with DIP: 18.104.22.168. To "route" this packet, Destination Network is detected: 22.214.171.124 AND Netmask for the first Routing table entry(ie, 255.255.255.0) 0001 0100.0000 0000.0000 0000.0000 0010 AND 1111 1111.1111 1111.1111 1111.0000 0000 = 0001 0100.0000 0000.0000 0000.0000 0000 ie, 126.96.36.199 [This matches the "network" entry in the Routing table and the packet is sent to router with address 188.8.131.52 Answer to Q3: Static routes are used when you explicitly want a particular next hop to be taken instead of leaving it to the configured routing protocol(like, ospf). Moreover, scaling of the network with static routing is difficult as more effort is required. Also, as MaQleod said, it is not fault tolerant.

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An important strategy to use before, during and after reading to enhance interest and comprehension* Engaging students in a dialogue about something they are about to read can clarify their thinking and help you find out what they already know or expect from the material. Questions and discussion also clarify understanding during and after reading. One way to begin this dialogue is through asking questions that elicit responses reflecting the student's thoughts and understandings about the reading. Too often questions are used only at the end of reading, asked by the teacher or tutor to check comprehension. In fact, successful readers ask themselves questions throughout the reading process. Beginning readers need modeling and practice to learn how to do this. Effective questions encourage real thinking, not just yes or no answers. Notice too that different kinds of questions require different ways of finding the answer: - Factual or "right there" questions can be answered with a single word or phrase found right in the story: "When did the story take place?" "It was midnight, the 25th of October..." - Inference or "think and search" questions require finding and integrating information from several places in the story and relating one's own knowledge as well. "When did the story take place?" "The harvest moon hung high in the sky, shining on the field of ripe orange pumpkins waiting to be picked for Halloween..." Using our background knowledge of concepts like "harvest" and "Halloween" as well as the words "ripe pumpkins" we figure out that this story takes place one night in late October, even though those words aren't used in the text. - "In the head" or "On my own" questions require bringing in one's own information, (background knowledge). These can be answered without reading from the book. "We have read a lot of fairy tales, what kinds of things usually happen in fairy tales?" Or, "You told me you have a cat. What might happen in a story called Puss in Boots? Do you think it could be true?"' - Remember to focus on the positive aspects of the child's responses to encourage future attempts. Questions before reading should help the reader: - Make connections between background knowledge and the topic of the book: "This book is about Anansi the Spider: do you remember the other Anansi book we read? What kind of character is Anansi? What kinds of things did he do in that story? How do you suppose he will behave in this book?" - Set a purpose for reading: "Here is a new book about sea turtles. What are some things that you would like to learn about these creatures?" - Make predictions: "The title of this book is The Missing Tooth, (Cole, 1988). Who do you suppose the two boys on the cover are, and what do you think this book might be about? What happens to you when you lose a tooth?" Questions during reading should help the reader: - Clarify and review what has happened so far: "What are some of the things that made Arlo and Robby such good friends?" - Confirm or create new predictions: "Now that one boy has lost a tooth, so they aren't both the same, what's going to happen? I wonder if they will stay friends:" - Critically evaluate the story and make personal connections: "Could this really happen -- that two good friends could have a fight because one of them had something the other wanted? How would you feel if you were Robby? What would you do?" - Make connections with other experiences or books: "Does this remind you of another story/character, what happened in that story? Could that happen here?" - Monitor the child's reading for meaning and accuracy: "Did that word 'horned' make sense? What is a 'horned toad'?" Questions after reading will help: - Reinforce the concept that reading is for understanding the meaning of the text, and making connections: "In this story about Amy's first day in school how did she feel before going into her classroom? How did you feel on your first day?" - Model ways of thinking through and organizing the information they have taken in from reading a text: "What did Amy's teacher do when she walked into the classroom? How does Amy feel now? How do you know that?" - Encourage critical thinking and personal response: "What do you think might have happened if the teacher had not done that? Why do you think the author decided to write this story? Would you have done what Amy did?" - Build awareness of common themes and structures in literature: "What other story or character does this sound like? What parts are the same? What parts are different?" When children respond to your questions it is important to listen carefully to what they say, and to respond to any questions they may have. Also, if a student has misunderstood a section of a story you may want to go back to that part of the book and reread it, clarifying any difficult vocabulary if necessary, to help the student understand what is going on. You might say: "You said that the rabbit was laughing at the pig at the end, but you know, I remember something different. Lets look at that part of the book again and see what it says." (Then reread the appropriate segment of the book.) "Here it says: 'The rabbit ran through the door and slipped past the man who was laughing at the pig.' Do you know what it means when someone "slips past" something?..." The most important thing, however, when talking about a story with a child is to let them know that their ideas about what they have read are important and that you value what they have to say. *These suggestions are adapted from: R. Huntsman, 1990; L. Rhodes and C. Dudley-Marling, 1996.

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A movement for more democracy in American government in the 1830s. Led by President Andrew Jackson, this movement championed greater rights for the common man and was opposed to any signs of aristocracy in the nation. Jacksonian democracy was aided by the strong spirit of equality among the people of the newer settlements in the South and West. It was also aided by the extension of the vote in eastern states to men without property; in the early days of the United States, many places had allowed only male property owners to vote. (Compare Jeffersonian democracy.) In the Northwest territory, the old home of jacksonian democracy, they overtopped agriculture. All this and his steady advocacy of jacksonian democracy constituted him no paltry antagonist. This provision stood clear in the document; but judicial ingenuity had circumvented it in the age of jacksonian democracy. Crockett was a Southerner and, as has been stated, at first a friend of the jacksonian democracy.

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Common Core Standards: Math High School: Geometry Similarity, Right Triangles, and Trigonometry G-SRT.1b b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. The next order of business is the scale factor, which is a number that compares the sizes of two similar objects. Students should know that we can find the scale factor by dividing the lengths of the corresponding sides in the similar objects or by comparing the distance from the center of dilation to each object. For instance, a scale factor of 2 means that one of the objects is twice as big as the other. Students should know that dilations can make larger or smaller objects. If a larger object is created, we say that it's been expanded (the scale factor is greater than 1) and a smaller object results from contraction (the scale factor is less than 1). Scale factors and dilations are used together when discussing and, in essence, defining similarity. If students aren't sure what you're asking them to do, we suggest going through it step by step with a simple shape like a triangle or quadrilateral. Then, you could even have them measure the side lengths of the two images and he distances from the center with a ruler to come up with a scale factor. Hopefully, an activity like that will tie all these concepts together.

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17,500-year-old shells from a clam found in North Atlantic seafloor sediment helped WHOI geologist Lloyd Keigwin learn about ocean circulation and climate changes. Clams and other shelled organisms incorporate the chemical characteristics of the deep-ocean water that existed when their shells and skeletons formed. (Photo by Lloyd Keigwin, Woods Hole Oceanographic Institution) An 82-foot (25-meter) seafloor sediment core is recovered during a 2004 cruise onboard the research vessel Knorr. The hollow tube plunges into the seafloor, where it is filled with a sample of layers of sediments that accumulate over hundreds and thousands of years. The sediments contain clues to past ocean and climate changes. (Photo by Lloyd Keigwin, Woods Hole Oceanographic Institution) Today (top), the oceans? overturning circulation carries a tremendous amount of heat northward, warming the North Atlantic region. It also generates a huge volume of cold, salty water called North Atlantic Deep Water?a great mass of water that flows southward, filling up the deep Atlantic Ocean basin and eventually spreading into the deep Indian and Pacific Oceans. Paleoceanographers have found evidence for very different patterns of ocean circulation in the past. About 20,000 years ago (bottom), waters in the North Atlantic sank only to intermediate depths and spread to a far lesser extent. When that occurred, the climate in the North Atlantic region was generally cold and more variable. (Illustration by E. Paul Oberlander, Woods Hole Oceanographic Institution)

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Greenland Ice Sheet Today offers the latest satellite data on surface melting of the Greenland Ice Sheet. Surface melt on the ice sheet results from daily weather conditions that are driven by air temperatures, winds, and feedback effect from changes in the snow or surface dust and soot. The extent and duration of this surface melting is an indicator of changing climate and other conditions. It is a major component of the waning of the ice sheet. The Greenland Ice Sheet is very thick, averaging 2 to 3 kilometers (1 to 2 miles) across most of the island. Ice sheets normally experience cycles of accumulation from snowfall, and melt due to seasonally warm conditions. In the balance, the average mass of an ice sheet may change very little—unless a changing climate is tipping the balance towards melt. The mass of ice in the Greenland Ice Sheet has begun to decline in recent decades, attended by an increase in surface melt. At high elevations on the ice sheet, an increase in winter snow accumulation has partially offset the melt. However, the mass loss at lower elevations is outpacing the greater accumulation at high elevations, because warmer temperatures have led to increased melt and faster glacier movement at the island’s edges. Researchers monitor many types of satellite data on melting in Greenland to understand how melt patterns may be changing. While local melting can occur on Greenland at any time of the year, the main melt season is June through August. A slight amount of melt usually begins at several places along the southwestern coast in April and May. In early June, the melt begins to spread northward, eastward along the coast, and into the interior. Melting is most extensive in July, and meltwater lakes typically form along the western flank of the ice sheet, visible in satellite images. High elevation areas (above 2,000 meters, or 6,000 feet) may see brief periods of melting in July and early August, but the highest elevation regions (near 3,000 meters, or 10,000 feet) almost never melt. The melt season typically ends by November. In July 2012, a very unusual weather event occurred. For a few days, the entire ice sheet indicated surface melting. While evidence of past heat waves similar to this can be found in ice core records, it had never been seen in the satellite monitoring period (1979 to present). Overall, the 2012 melt season far exceeded all previous years of monitoring, and led to significant amounts of loss of the ice sheet for the year. This event prompted NSIDC to build this Web site, with the help of two prominent experts on Greenland surface melting (Dr. Thomas Mote of University of Georgia, and Dr. Marco Tedesco of CUNY). Ice sheet facts An ice sheet is a mass of glacial land ice extending more than 50,000 square kilometers (20,000 square miles). The two ice sheets on Earth today cover most of Greenland and Antarctica. Greenland has been covered in ice for more than 18 million years; the current ice can be as old as 100,000 years old. Together, the Antarctic and Greenland ice sheets contain more than 99 percent of the freshwater ice on Earth. The Greenland Ice Sheet extends about 1.7 million square kilometers (656,000 square miles), covering most of the island of Greenland, three times the size of Texas. Ice sheets contain enormous quantities of frozen water. If the Greenland Ice Sheet melted completely, scientists estimate that sea level would rise about 6 meters (20 feet).

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Electronics Measurement: Ohm's Law The term Ohm's law refers to one of the fundamental relationships found in electronic circuits: that, for a given resistance, current is directly proportional to voltage. In other words, if you increase the voltage through a circuit whose resistance is fixed, the current goes up. If you decrease the voltage, the current goes down. Ohm's law expresses this relationship as a simple mathematical formula: In this formula, V stands for voltage (in volts), I stands for current (in amperes), and R stands for resistance (in ohms). Here's an example of how to calculate voltage in a circuit with a lamp powered by the two AA cells. Suppose you already know that the resistance of the lamp is 12 Ω, and the current flowing through the lamp is 250 mA, which is the same as 0.25 A. Then, you can calculate the voltage as follows: Ohm's law is incredibly useful because it lets you calculate an unknown voltage, current, or resistance. In short, if you know two of these three quantities you can calculate the third. Go back (if you dare) to your high-school algebra class and remember that you can rearrange the terms in a simple formula such as Ohm's law to create other equivalent formulas. In particular: If you don't know the voltage, you can calculate it by multiplying the current by the resistance. If you don't know the current, you can calculate it by dividing the voltage by the resistance. If you don't know the resistance, you can calculate it by dividing the voltage by the current. To convince yourself that these formulas work, look again at the circuit with a lamp that has 12 Ω of resistance connected to two AA batteries for a total voltage of 3 V. Then you can calculate the current flowing through the lamp as follows: If you know the battery voltage (3 V) and the current (250 mA, which is 0.25 A), you can calculate the resistance of the lamp like this: Wasn't going back to high school algebra fun? Next thing you know, you're going to start looking for a prom date. The most important thing to remember about Ohm's law is that you must always do the calculations in terms of volts, amperes, and ohms. For example, if you measure the current in milliamps (which you usually will in electronic circuits), you must convert the milliamps to amperes by dividing by 1,000. For example, 250 mA is 0.25 A. Here are a few other things you should keep in mind concerning Ohm's law: Remember that the definition of one ohm is the amount of resistance that allows one ampere of current to flow when one volt of potential is applied to it? This definition is based on Ohm's law. If V is 1 and I is 1, then R must also be 1. If you wonder why the symbols for voltage and resistance are V and R, which make perfect sense, but the symbol for current is I, which makes no sense, it has to do with history. The unit of measure for current — the ampere — is named after André-Marie Ampère, a French physicist who was one of the pioneers of early electrical science. The French word he used to describe the strength of an electric current was intensité – in English, intensity. Thus, amperage is a measure of the intensity of the current. Hence the letter I. In the interest of international cooperation, the term volt is named for the Italian scientist Alessandro Volta, who invented the first electric battery in 1800. (Actually, his full name was Count Alessandro Giuseppe Antonio Anastasio Volta.)

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Lesson 5: What Makes an Amendment? Students will learn about the process of amending the Constitution. They will review the details of the amendment process and discuss its pros and cons. In class activities, assignments, and the Lesson Extensions, student partners and groups will create persuasive presentations that they will share with the class to gain support for an amendment. Students will also learn about the political process and how it relates to the powers of the government, in that civic participation is necessary in a democratic society and strengthens a constitutional government. Students will develop the ability to make reasoned and informed decisions about their own personal freedoms in balance with the stability of the common good, understand the influence of the past and its historical significance, and grasp the issues of the present. Write the question below on the board. Explain that the lesson activities are geared to help students explore and then respond to this question later during the Lesson Wrap-up. Skills Supporting Common Core State Standards for English Language Arts and History/Social Studies: - Identify key ideas and inferences along with text support - Determine the central idea - Provide a summary - Trace and evaluate arguments - Participate in group discussions - Follow rules for discussions, set goals and deadlines, and define role - Pose and respond to questions - Review ideas from more than one perspective - Distinguish claims through reason and evidence - Present claims and findings - Adapt speech to fit the context of a task 45 minutes for the main activities; 15 minutes for Lesson Extension 1; 30 minutes for preparation of Lesson Extension 2 (in-class or out-of-class assignment) and 15 minutes for oral class presentation - Amazing Amendments Reproducible - Internet access - copy of the U.S. Constitution: archives.gov/exhibits/charters/constitution.html - copy of the Bill of Rights: archives.gov/exhibits/charters/bill_of_rights_transcript.html - copy of the Constitutional Amendment Process: www.archives.gov/federal-register/constitution Activity Directions (Part 1): • Remind students that Article V of the Constitution allows for the document to be amended. Provide the text in print or online (see Materials for document link) for students to use as reference. Write the word “amendment” on the board and ask students to define it. Guide discussion toward the definition as “a change or addition to a constitution.” Help students understand that as a living document, the Constitution may change just as people change over time. (If your classroom has online access, take a few moments to show students the website for the constitutional amendment process; see Materials for the document link.) Open a brief discussion on this concept by asking the following question: • Then distribute the Amazing Amendments Reproducible. Direct students to the chart at the top of the handout. Point out that Article V explains the two ways to make amendments to the Constitution. Read Article V aloud and then walk the class through the steps presented in the chart, as supported by the text in Article V, as follows: - The first way is through Congress. Two-thirds of Congress (made up of the House of Representatives and the Senate) can propose, or ask for, an amendment. - The second way is through the states. Two-thirds of the state legislatures can call for an official meeting to propose an amendment. - When the meeting is called, the amendment is then presented. - Once an amendment receives the required number of votes in Congress or from the states, it must then be ratified (approved) by three-fourths of all state legislatures or three-fourths of special state conventions. That means that 38 states would have to accept the amendment once it is proposed in order for it to be added to the Constitution. - The legislative branch (Congress) - 50 states x three-fourths majority = 38 states needed - Get two-thirds of all state legislatures to ask for a meeting to propose the amendment, call a special convention and propose the amendment, and get three-fourths of all state legislatures or special state conventions to ratify the amendment. • Conclude this part of the lesson with an open discussion based on one or more of the following questions: Does it seem fair? How does it create checks and balances within the government’s legislative process? Activity Directions (Part 2): • Divide students into two groups, Group A and Group B. Have Group A discuss how they would resolve a point of disagreement or a contentious issue. Ask them to consider how they would approach this issue. Would they present evidence? How would they argue their point of view? Before the groups begin their discussions, explain that taking the best approach to resolving differences and supporting a belief is just what legislators do when they propose amendments and work on a strategy to support their proposals. • Have students in Group B write the words “persuasion,” “compromise,” “consensus building,” and “negotiation” on large pieces of paper that look similar to Olympic scorecards. Have Group B listen to and observe Group A’s discussion. As Group B listens and observes Group A, have members of Group B hold up the appropriate sign identifying or best representing the process they observe within Group A’s discussion as it progresses. • After 10 to 15 minutes, have the groups switch places. Ask students to discuss this experience and what they learned about building consensus within a group. In particular, have them address the following questions: When was it important to speak, and when was it important to listen? • Lesson Extension Alert: To have student pairs further explore the ideas that have been proposed as amendments to the Constitution, see Lesson Extension 2. Wrap-up With the Essential Question: Return to the Essential Question that was written on the board at the beginning of the lesson. Open a discussion in which students respond to this question, based on their class experience. Encourage students to support their responses with text and details from the Constitution and the Bill of Rights. • To demonstrate the complex, difficult amendment process, have students work in groups to get their own amendments ratified. Explain to students that they will be working in groups of three to develop their own amendments, which the class will vote on. You may allow class time for group meetings; during those meetings, groups can assign members tasks that may be completed out of class. Have every group member participate and divide up the work to be completed at home. • Tell students that as they develop their amendments they should answer the following questions that you write on the board. Students should copy them onto the backs of their completed Amazing Amendments Reproducibles: What secondary source material or evidence can you supply that demonstrates its necessity or importance? Who will support the amendment? Why? How will the amendment be relevant in the future? Will it be able to last 200 or more years like the Bill of Rights? What has changed about the United States since the original Constitution was written that makes this amendment relevant? • Encourage students to develop creative proposals to gain support for their amendments. They can create posters, slogans, songs, etc. to support their amendments, as long as the amendment is beneficial to the United States and its people. You can add some time to the due date for this assignment to give students ample time to develop their amendments and campaign in their support. • During the class period when the assignment is due, have each group present its amendment to the class. Encourage students to ask the group questions about their amendments. Instruct students to write down their thoughts about each amendment as it is presented. Once all groups have made their presentations, hand out a ballot with each amendment listed. Have students vote on the amendments and turn in their ballots without showing anyone else. • Have students add up the number of voters and determine how many votes will be needed to constitute a three-fourths majority. Inform students that they will need that many votes in order to get their amendments ratified. Now tally the votes and see which amendments passed! • End the in-class portion of this assignment by asking students if their opinions about amending the Constitution have changed now that they have tried the process themselves. (1) To appreciate the historical context of the amendment process, share the following material with the class: James Madison, the fourth president of the United States, was also called “the father of the Constitution.” In 1789, while a leader in the House of Representatives, he wrote the first draft of the Bill of Rights, including the Sixth and Seventh Amendments. His draft included a total of 12 amendments, not just the 10 we know as the Bill of Rights. Madison proposed these amendments to Congress in June 1789. A few months later, the House of Representatives and the Senate both voted in favor of the amendments. On September 25, 1789, the amendments were proposed to the states. There were 13 states in the United States at that time. Ten of the 12 amendments, including the Sixth and Seventh, were ratified by most of the states. In November 1789, New Jersey became the first state to ratify the Bill of Rights. Other states soon followed and, in 1791, 11 out of the 14 states (up from 13 states, with Vermont entering the Union by 1791), or 79 percent, had ratified 10 of the 12 amendments. The Bill of Rights was then added to the Constitution. One of the two Bill of Rights amendments that was not ratified at the time eventually became the Twenty-Seventh Amendment. This amendment of 1789 limited when members of Congress could change their salaries. Like the Sixth and Seventh Amendments, it was proposed to the states in 1789, but it was not ratified until 1992, more than 200 years later! By 1791, six states had approved the amendment, far less than the 11 needed for ratification. By the time it was ratified, over 74,000 days had passed since it was proposed, and 36 states had been added to the country. In comparison, the Twenty-Sixth Amendment, lowering the voting age to 18, took only 100 days to ratify. • Explain to students that thousands of amendments have been proposed since the Constitution was written, but only 27 have been ratified by the states. Conclude this presentation by asking students whether they think it is good or bad that amendments are so difficult to ratify. Lead a discussion about the pros and cons of the amendment process. Ask students if they think the process should be changed. Encourage students to share their ideas with the class. (2) Have students work with partners to research in the library or online an amendment that was proposed to the states but never ratified. Remind students to note the source or sources from where they received their information and to cite the sources on notes that include information they learned from them. Direct student partners to develop a brief oral presentation that describes what the amendment was, when it was proposed, and why it failed. As part of the oral presentation, ask one partner to develop and present a persuasive oral argument in favor of the amendment, and the other partner to develop and present a persuasive oral argument opposed to it. These pro and con arguments may be presented to the class for further debate about whether the proposals would be a good amendment to add to the Constitution now.

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view a plan This is an introductory economics lesson on wants, needs, resources and scarcity Title – Wants, Needs, Resources and Scarcity By – Joel Crosby Primary Subject – Social Studies Grade Level – 12 Economics Introduction to Economics Course (First Unit) Lesson Duration: 90 minutes - The purpose of this lesson is to introduce the topic of economics to the students. They will learn what the word “economics” means as well as a few terms that make up the foundation of economics. - The focus of the lesson will be on the key economic factors of wants , needs , resources and scarcity . This will provide a foundation of knowledge for students to build on as they go through the course. Illustrate the relationship between: - scarcity and limited resources - unlimited human wants and the economic choices made by individuals, families, communities and nations including: - how families must budget their income and expenses - how people use psychological and intellectual resources to deal with scarcity - how local political entities as well as nation-states use scarce resources to satisfy human wants. (E, G) Student Lesson Objectives: The student will be able to: - define key economic terms including scarcity, wants/needs, and resources - identify examples of the above terms in their own lives - create a monthly budget - Video projector for video clips - Readily accessible video clips combining economics with humor and music such as: - Scarcity http://www.youtube.com/watch?v=W35X_vddDjQ - Paper and Pencils/Pens - Dry erase board/markers - Define the word ” economics ” on the dry erase board. Explain that economics is a part of everyone’s life. Explain that economics has affected students from the day they were born and will continue to affect them until the day they die. (5 minutes) - To start students thinking about economics, have them create an individual “KWL” chart for “what they know,” “what they want to know,” and finally at the end of class, “what they have learned” from the lesson. (5 minutes) - Have students take out another sheet a paper to list everything they could ever want in the world in 10 minutes. (10 minutes) - Go over these lists as a class and make a list on the board of all the different wants. (5 minutes) - Explain the definition of economics on the board and compare it to the list of wants/needs. Explain how their lists reflect humanity’s never-ending ” wants/needs/demands .” In a call and answer session, ask the students to consider what of their lists may be feasible to attain and what could likely never happen. Now, define the term ” scarcity ” on the board and explain to students that scarcity of a variety of ” resources ” such as land and money prevent us from getting what we want. (10 minutes) - Show students two 4-6 minute video clips that combine economics with humor and music. Instruct students to identify at least five wants that were shown in the videos as well as two ” resources ” that were mentioned. (15 minutes) - Briefly go over what the students wrote and examples for wants/needs and scarcity. (5 minutes) - Split the class into groups of four. The groups will create a budget that includes payments for power and rent as well as car payments, etc. in one column and the average monthly price they expect to pay in another column. Go over these worksheets with the class and evaluate which ones are more possible and how much salary it would take a year to be able to afford their budget. (25 minutes) - Bring students back to the KWL sheet that they began at the beginning of class. - To complete the “l” or “learned” portion of the KWL, students participate in a “graffiti board” activity in which the students write down a short sentence about what they have learned. - The teacher then goes over the “graffiti board” with the students to summarize the lesson. (10 minutes) - Assess students informally throughout the lesson through call/answer questions and for participation within their groups - Be sure to make it known that the board definitions will become test questions and that the notes taken from class should be kept to be studied later. - Also, have the students turn in their notes from the two short movies for a participation grade for those who paid attention. E-Mail Joel !

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The Fifteenth Amendment to the United States Constitution, October 8, 1869 The Fifteenth Amendment to the United States Constitution was the third of the three so-called Reconstruction amendments to settle constitutional questions that the Civil War had created. The Thirteenth Amendment, ratified in 1865, abolished slavery forever in all of the United States. The Fourteenth Amendment, ratified in 1868, is the longest and most complex of the amendments and has had the most wide-ranging and controversial influence on American politics and society. The Fifteenth Amendment granted voting rights to African American men, providing the most important key to participation in the American democratic process to millions of formerly enslaved, and politically excluded, people. Approved by the United States Congress in February 1869, the Fifteenth Amendment has two provisions. Section one states that a citizen's right to vote should not be denied “on account or race, color, or previous condition of servitude.” The second section of the provision gives the U.S. Congress the right to enforce the legislation. As with all proposed amendments to the U.S. Constitution, the proposed Fifteenth Amendment had to be ratified by three-fourths of the states, 28 of 37, in order to go into effect. There was some question about the willingness of former Confederate states to approve the new legislation. To guarantee compliance, Republican legislators amended the Reconstruction bills for three states—Mississippi, Texas, and Virginia—mandating ratification of the Fifteenth Amendment as a prerequisite of their readmission to the Union. Virginia, which had already drafted a state constitution that provided for universal manhood suffrage, ratified the Fifteenth Amendment on October 8, 1869. Within a year of passing Congress, all of the formerly Confederate states, except Tennessee, had ratified the provision. Secretary of State Hamilton Fish officially recorded the addition of the newest amendment to the U.S. Constitution on March 30, 1870. This broadside included Secretary Fish's message to Congress validating the Fifteenth Amendment, with a special message from U.S. president Ulysses S. Grant. Calling the amendment “the most important event that has occurred since the nation came into life,” Grant urged whites not to interfere with the enforcement of the new provision, and reminded African Americans of their responsibilities as voters. News of the Fifteenth Amendment's passage was greeted with jubilation in the African American communities. There were major parades in New York and Baltimore to mark the occasion, as well as commemorative events in subsequent years to mark the anniversary. The expansion of the franchise also had the immediate effect of increasing the number of African American men serving in public office. It is estimated that between the ratification of the Fifteenth Amendment and the end of Congressional Reconstruction in 1877, about two thousand African Americans served in local and state government offices, including state legislatures, and as members of Congress. These gains, however, proved difficult to maintain, especially in the face of increasing white hostility to progress made by African Americans. By late in the nineteenth and early in the twentieth centuries, as northern Republicans grew weary of interceding in the political and racial conflicts in the South, southern whites successful engineered, through the law and through force, a return to “home rule.” Legislatures throughout the South instituted provisions like literacy tests, poll taxes, and “grandfather clauses” in their constitutions, effectively limiting the eligibility of African American men, and scores of white men, to vote and hold elected office. What was not accomplished through the law was accomplished through threats, intimidation, and violence, mainly at the hands of groups like the Ku Klux Klan. Not until the civil rights movement in the 1950s and 1960s—a period sometime referred to as American's Second Reconstruction—were most African Americans able to regain this lost political ground. The ratification of the Twenty-fourth Amendment to the U.S. Constitution in 1964 outlawing the poll tax in federal elections, and the passage of the Voting Rights Act in 1965 (not to mention the earlier passage of the Nineteenth Amendment in 1919 also giving black women the right to vote) were meaningful steps in restoring to America's black citizens the protections necessary to secure their right to vote, and to participate effectively in America's democratic process. 1. What is the significance of the Fifteenth Amendment? What does it do? Where did it fall short? 2. What is the relationship between the Fourteenth and Fifteenth Amendments? How do they complement one another? 1. Discuss the connection between voting rights and civil rights. Use examples from the Reconstruction era and the Civil Rights era to examine the impact of the franchise throughout Virginia's and America's history. 2. Within the political system of the United States, why is it important to be able to elect your own representatives? What happens if large numbers of citizens are not able to have their views represented in the democratic process? Lowe, Richard. Republicans and Reconstruction in Virginia, 1856–70. Charlottesville: University Press of Virginia, 1991.

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Whales and dolphins are notoriously hard to study; they spend most of their lives underwater, travel great distances, and can be hard to see at sea. Furthermore, it's often tough to accurately calculate distance and identify species and sex from the deck of a research vessel. But a new proof-of-concept paper in PLoS ONE suggests a different method: using satellites to identify and track marine mammals. For this pilot study, the scientists chose to study southern right whales, a species that is large, slow, and relatively easy to identify. They used just one satellite image, taken in 2012 by WorldView2. It’s a massive, very high-resolution image of a known breeding area off the coast of Argentina. First, the researchers simply counted the objects in the image that might be whales, identifying 55 probable whales and 23 possible whales. Then they used image processing software to test how well computer programs could perform the same task. At best, this approach identified nearly 85 percent of the probable whales that the researchers had found, as well as 89 percent of the possible whales. A 2002 study evaluating the utility of satellites in cetacean research had very limited success, but this study is much more promising thanks to improved satellite technology and better image processing abilities. However, there are still issues inherent in counting animals from space. The analysis in this study yielded several false positives—rocks or flocks of birds that matched the relative shape and size of a whale. Researchers will need to be familiar with the animal they are looking for and know what else is in the area so that they can distinguish between the desired species and other objects in the image—living and non-living. It’s also currently unclear how deep in the water column whales can be detected via satellite images. But as satellite technology continues to advance and as researchers strive to improve their methodology, it’s likely that the use of satellites to study whales and other elusive species will play a large role in biology and conservation in the future.

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By analyzing carbonate minerals in a four-billion-year-old meteorite that originated near the surface of Mars, the scientists determined that the minerals formed at about 18°C.Because Mars now has an average temperature of -63°C, the existence of liquid water in the past means that the climate was much warmer then. The researchers analyzed one of the oldest known rocks in the world: ALH84001, a Martian meteorite discovered in 1984 in the Allan Hills of Antarctica. The meteorite likely started out tens of meters below the Martian surface and was blown off when another meteorite struck the area, blasting the piece of Mars toward Earth. The rock made headlines in 1996 when scientists discovered tiny globules in it that looked like fossilized bacteria. But the claim that it was extraterrestrial life didn't hold up. The mild temperature means that the carbonate must have formed in liquid water. Could this wet and warm environment have been a habitat for life? Most likely not, the researchers say. These conditions wouldn't have existed long enough for life to grow or evolve—it would have taken only hours to days for the water to dry up. Ref. Carbonates in the Martian meteorite Allan Hills 84001 formed at 18 ± 4 °C in a near-surface aqueous environment. 2011. I. Halevy, et al. PNAS 108: 16895-16899.

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CAUSE AND EFFECT This is also good lesson to use in order to teach or review cause and effect. ELL students can learn the signal words for cause and effect, such as: because, so, since (beginning level), led to, brought about, produced (intermediate level), as a result of, so that, since, therefore (advanced level). Teacher and students can list causes and effects of the cotton gin. Then students can put a sentence together using the list and a signal word. Teacher can also put these phrases on index cards and students can go around the room finding the partner that matches either their cause or their effect (these are written on the index card). Next, the students can put their cause and effect in a sentence or several sentences using different signal words for cause and effect. Examples: The cotton gin took the seeds out of cotton easier and faster, therefore more cotton could be cleaned per day. Since the cotton gin took the seeds out of cotton easier and faster, more cotton could be cleaned per day. Because more cotton could be cleaned per day, more slaves could be used to pick cotton. The cotton gin brought an increased production of cotton. More slaves were needed to pick cotton as a result of the invention of the cotton gin. Students can also write a newspaper article featuring their new invention. A book entitled, The Inventors Times by Dan Driscoll and James Zigarelli, published by Scholastic Books, is great for showing examples of newspaper articles that feature new inventions. Below are two graphs. The first graph shows the rise of cotton production in the South and the rise in the number of slaves. The second graph shows what percentage of the Souths exports was cotton. Students should notice that as the cotton production increased, so did the need for slaves. Is it good to have an economy so dependent on one crop or skill? What other countries have had similar experiences with a one crop or skill economy? What effect did it have on them? Have students deduce from the graphs the effect of the cotton gin on the South, their economy, and even the change in their way of life. If your students are advanced or GATE, you can have students research the growth in the outsourcing of jobs in the United States to other countries and deduce what effect that is having and willhave in the United States.

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This tip on improving your SAT score was provided by Vivian Kerr at Veritas Prep. It can feel as if there are a lot of formulas and concepts tested on the SAT, but Coordinate Geometry is pretty predictable. We have to know the standard equations of lines, parabolas, and circles graphed on a coordinate plane, and we have to know how to find the midpoint and distance between points on those shapes. Distance Formula = We use this to find the distance between any two points (x1, y1) and (x2, y2). Note how it’s basically a derivative of the Pythagorean Theorem (imagine drawing a right triangle so that the distance between these points is the hypotenuse). Midpoint Formula = Use this to find the midpoint between two points (notice how you are essentially finding the average of the x-coordinates and the average of the y-coordinates). Another big concept when we’re talking about lines is slope. The slope is described as Rise / Run or Change in y / Change in x. As long as you know any two points on a line, you can find the slope. Remember that parallel lines have the same slope, and perpendicular lines have negative reciprocal slopes. y = mx + b This is called slope-intercept form. An equation in this form will always make a straight line on a graph (note how neither x nor y have an exponent). In this form, b is the y-intercept (the point on the y-axis where the line crosses) and m is the slope. y = ax 2 + bx + c This is the standard equation for a parabola. In this equation, c represents the y-intercept. A standard equation in which a variable is squared will never make a straight line. (x – h)2 + (y – k)2 = r2 This is the standard equation for a circle. Here (h, k) is the center point of the circle and r is the radius. Notice that inside the parentheses, we are subtracting “h” and “k” when on the graph, “h” and “k” are both positive. If “h” and “k” were negative, we would add them inside the parentheses. On test day, you may be given parameters and asked the question: 1. What is the equation of a circle with a center at (4, -5) and a diameter of 16? To solve, let’s start with our standard equation: (x – h)2 + (y – k)2 = r2 The radius is half the diameter in a circle, so the radius would be 8. 82 = 64. We’re going to take the opposite sign inside the parentheses (since “4” is positive we will subtract it, and since “-5” is negative we will add it). The correct answer is (x – 4)2 + (y + 5)2 = 64. Remember that any straight line can be described by the equation y = mx + b. On test day, as long as you have two coordinates of a line, you can always find its equation. For Coordinate Geometry question practice, take a full-length SAT practice test to sharpen your skills.

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Have your child draw a story map (a diagram that shows the events of a story in order of occurrence) to help him sequence the beginning, middle and end of a story. Sequencing is the ability to see the order of events, which helps reading comprehension. What you’ll need: - A book to read aloud - Drawing paper - Art materials such as crayons, markers and paints Here’s How To Do It Choose a book to read aloud with your child. Before reading tell your child to think about the events of the story. After reading discuss with your child what happens in the beginning, middle and end of the story. You can revisit the story with your child to gather information; try looking at the pictures or rereading passages. On paper have your child draw or paint the three events in order with an arrow between each drawing to represent the sequence of events. This is often called a “story map” in elementary classrooms. Your child can also write or dictate to you captions under each drawing or painting.

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Bring Science Home: Activity 11 From National Science Education Standards: Earth's history The surface of the moon is full of jagged craters. This rough surface comes from millions of years of collisions with rocks—called meteors—that crash into its surface. Why doesn't Earth's surface look like that? Earth's surface does have some evidence of meteorites, such as the massive Meteor Crater site in Arizona. That crater is about 4,000 feet (1,219 meters) across and about 570 feet (174 meters) deep. So does that mean that was the size and shape of the meteor that crashed there? Nope! It was much smaller than that. With this fun activity, you can use small snacks to study this striking feature of Earth's—and the moon's—surface. When you watch a meteor shower, most of the streaks of light (or "shooting stars") that you see are actually small rocks burning up in Earth's atmosphere. Most of them don't reach the ground, but those that do are called "meteorites." These rocks are traveling so fast (thousands of miles per hour) that they hit the ground with an amazing amount of force. That force is usually enough to move a lot more dirt than the size of the meteorite itself: the crater. The meteorite that created the 4,000-foot-wide Meteor Crater in Arizona was probably only about 164 feet (50 meters) in diameter (really big for a rock falling from outer space, but still only a fraction of the size of the crater it created). Scientists estimate that this impact event occurred about 50,000 years ago—long before there were humans living in the area. The moon has a lot more visible impact craters because it doesn't have an atmosphere to burn up smaller incoming rocks. The moon also does not have liquid water or an active crust (with volcanoes and other forces) to alter the surface and remove evidence of past impacts. These agents helped to smooth out many of the meteorite craters here on Earth in the billions of years since the planet formed. • Large shallow pan or tray with edges • Dry pudding mix, dry drink mix or cocoa powder or another powder that is a different color • Roundish nuts, seeds and/or small fruits (such as raisins, almonds, peanut halves, cherries, and so on) • Sifter or sieve • Fill the large pan or tray with an inch or two of flour. • Cover that layer with a dusting of the second, different-colored powder using a sifter. This layer will be like the top level of "dirt" on the surface. • Assemble your collection of mini "meteors." • Hold one of your mini meteors a couple feet above the flour tray. When the meteor falls, what do you think it will do to the surface? • Drop the meteor (when it hits the surface, it becomes a meteorite). What happened? • What happens when the meteor falls faster? Try dropping it from a higher point—or carefully throwing it downward toward the flour surface. • Now try different sized and shaped meteors. How are their craters different? How are they similar? • What does the pattern of "dirt" around your craters look like? Observations and results How did the size of the craters compare with the size of the meteorites that made them? Does a high-speed meteor make a different type of crater than a slow-speed meteor? Check both the size and shape. The material that gets moved (or ejected) during the impact is known as "ejecta." By studying the patterns in which lower levels of dirt and rock were tossed up by the impact, scientists can make estimates about how big the meteorite originally was. (Meteors often get incinerated upon impact or disappear over time.) Ask a friend or your parent to make several craters and remove the meteorites; can you estimate the size of the meteorite from the ejecta and the crater? Meteorites that survive their fall to the surface can also often tell us about where they came from by the type of rock and other chemicals they contain. For example, scientists have found some meteorites that are made up of the same material as the moon. Why doesn't Earth's surface look like that of the moon? Aside from most of the rock burning up in the Earth's atmosphere before it can hit the surface, craters on Earth often vanish over time as the Earth's surface changes from the flow of liquid water, scraping glaciers, lava-spewing volcanoes or other agents. The moon doesn't have a very active surface, so meteor craters or even footprints from astronauts are likely to stay as they are for a very long time. Share your mini meteorite strike observations and results! Leave a comment below or share your photos and feedback on Scientific American's Facebook page. Be careful not to spill the powder when throwing it away. More to explore Why Are Impact Craters Always Round? from Scientific American "Meteorite Nugget Pushes Back Age of the Solar System By Nearly 2 Million Years" from Scientific American "Meteor Showers: Where, When and How to Look for Them" activity for kids from The Planetary Society "Comets and Meteors" from the European Space Agency Kids Comets, Meteors and Asteroids by Seymour Simon, ages 4–8 Meteors and Comets by Gregory Vogt, ages 9–12

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In the previous section of Lesson 4, the vector nature of the electric field strength was discussed. The magnitude or strength of an electric field in the space surrounding a source charge is related directly to the quantity of charge on the source charge and inversely to the distance from the source charge. The direction of the electric field is always directed in the direction that a positive test charge would be pushed or pulled if placed in the space surrounding the source charge. Since electric field is a vector quantity, it can be represented by a vector arrow. For any given location, the arrows point in the direction of the electric field and their length is proportional to the strength of the electric field at that location. Such vector arrows are shown in the diagram below. Note that the lengths of the arrows are longer when closer to the source charge and shorter when further from the source charge. A more useful means of visually representing the vector nature of an electric field is through the use of electric field lines of force. Rather than draw countless vector arrows in the space surrounding a source charge, it is perhaps more useful to draw a pattern of several lines that extend between infinity and the source charge. These pattern of lines, sometimes referred to as electric field lines, point in the direction that a positive test charge would accelerate if placed upon the line. As such, the lines are directed away from positively charged source charges and toward negatively charged source charges. To communicate information about the direction of the field, each line must include an arrowhead that points in the appropriate direction. An electric field line pattern could include an infinite number of lines. Because drawing such large quantities of lines tends to decrease the readability of the patterns, the number of lines is usually limited. The presence of a few lines around a charge is typically sufficient to convey the nature of the electric field in the space surrounding the lines. Rules for Drawing Electric Field Patterns There are a variety of conventions and rules to drawing such patterns of electric field lines. The conventions are simply established in order that electric field line patterns communicate the greatest amount of information about the nature of the electric field surrounding a charged object. One common convention is to surround more charged objects by more lines. Objects with greater charge create stronger electric fields. By surrounding a highly charged object with more lines, one can communicate the strength of an electric field in the space surrounding a charged object by the line density. This convention is depicted in the diagram below. Not only does the density of lines surrounding any given object reveal information about the quantity of charge on the source charge, the density of lines at a specific location in space reveals information about the strength of the field at that location. Consider the object shown at the right. Two different circular cross-sections are drawn at different distances from the source charge. These cross-sections represent regions of space closer to and further from the source charge. The field lines are closer together in the regions of space closest to the charge; and they are spread further apart in the regions of space furthest from the charge. Based on the convention concerning line density, one would reason that the electric field is greatest at locations closest to the surface of the charge and least at locations further from the surface of the charge. Line density in an electric field line pattern reveals information about the strength or magnitude of an electric field. A second rule for drawing electric field lines involves drawing the lines of force perpendicular to the surfaces of objects at the locations where the lines connect to object's surfaces. At the surface of both symmetrically shaped and irregularly shaped objects, there is never a component of electric force that is directed parallel to the surface. The electric force, and thus the electric field, is always directed perpendicular to the surface of an object. If there were ever any component of force parallel to the surface, then any excess charge residing upon the surface of a source charge would begin to accelerate. This would lead to the occurrence of an electric current within the object; this is never observed in static electricity. Once a line of force leaves the surface of an object, it will often alter its direction. This occurs when drawing electric field lines for configurations of two or more charges as discussed in the section below. A final rule for drawing electric field lines involves the intersection of lines. Electric field lines should never cross. This is particularly important (and tempting to break) when drawing electric field lines for situations involving a configuration of charges (as in the section below). If electric field lines were ever allowed to cross each other at a given location, then you might be able to imagine the results. Electric field lines reveal information about the direction (and the strength) of an electric field within a region of space. If the lines cross each other at a given location, then there must be two distinctly different values of electric field with their own individual direction at that given location. This could never be the case. Every single location in space has its own electric field strength and direction associated with it. Consequently, the lines representing the field cannot cross each other at any given location in space. Electric Field Lines for Configurations of Two or More Charges In the examples above, we've seen electric field lines for the space surrounding single point charges. But what if a region of space contains more than one point charge? How can the electric field in the space surrounding a configuration of two or more charges be described by electric field lines? To answer this question, we will first return to our original method of drawing electric field vectors. Suppose that there are two positive charges - charge A (QA) and charge B (QB) - in a given region of space. Each charge creates its own electric field. At any given location surrounding the charges, the strength of the electric field can be calculated using the expression kQ/d2. Since there are two charges, the kQ/d2 calculation would have to be performed twice at each location - once with kQA/dA2 and once with kQB/dB2 (dA is the distance from that location to the center of charge A and dB is the distance from that location to the center of charge B). The results of these calculations are illustrated in the diagram below with electric field vectors (EA and EB) drawn at a variety of locations. The strength of the field is represented by the length of the arrow and the direction of the field is represented by the direction of the arrow. Since electric field is a vector, the usual operations that apply to vectors can be applied to electric field. That is, they can be added in head-to-tail fashion to determine the resultant or net electric field vector at each location. This is shown in the diagram below. The diagram above shows that the magnitude and direction of the electric field at each location is simply the vector sum of the electric field vectors for each individual charge. If more locations are selected and the process of drawing EA, EB and Enet is repeated, then the electric field strength and direction at a multitude of locations will be known. (This is not done since it is a highly time intensive task.) Ultimately, the electric field lines surrounding the configuration of our two charges would begin to emerge. For the limited number of points selected in this location, the beginnings of the electric field line pattern can be seen. This is depicted in the diagram below. Note that for each location, the electric field vectors point tangent to the direction of the electric field lines at any given point. The construction of electric field lines in this manner is a tedious and cumbersome task. The use of a field plotting computer software program or a lab procedure produces similar results in less time (and with more phun). Whatever the method used to determine the electric field line patterns for a configuration of charges, the general idea is that the pattern is the resultant of the patterns for the individual charges within the configuration. The electric field line patterns for other charge configurations are shown in the diagrams below. In each of the above diagrams, the individual source charges in the configuration possess the same amount of charge. Having an identical quantity of charge, each source charge has an equal ability to alter the space surrounding it. Subsequently, the pattern is symmetrical in nature and the number of lines emanating from a source charge or extending towards a source charge is the same. This reinforces a principle discussed earlier that stated that the density of lines surrounding any given source charge is proportional to the quantity of charge on that source charge. If the quantity of charge on a source charge is not identical, the pattern will take on an asymmetric nature, as one of the source charges will have a greater ability to alter the electrical nature of the surrounding space. This is depicted in the electric field line patterns below. After plotting the electric field line patterns for a variety of charge configurations, the general patterns for other configurations can be predicted. There are a number of principles that will assist in such predictions. These principles are described (or re-described) in the list below. - Electric field lines always extend from a positively charged object to a negatively charged object, from a positively charged object to infinity, or from infinity to a negatively charged object. - Electric field lines never cross each other. - Electric field lines are most dense around objects with the greatest amount of charge. - At locations where electric field lines meet the surface of an object, the lines are perpendicular to the surface. Electric Field Lines as an Invisible Reality It has been emphasized in Lesson 4 that the concept of an electric field arose as scientists attempted to explain the action-at-a-distance that occurs between charged objects. The concept of the electric field was first introduced by 19th century physicist Michael Faraday. It was Faraday's perception that the pattern of lines characterizing the electric field represents an invisible reality. Rather than thinking in terms of one charge affecting another charge, Faraday used the concept of a field to propose that a charged object (or a massive object in the case of a gravitational field) affects the space that surrounds it. As another object enters that space, it becomes affected by the field established in that space. Viewed in this manner, a charge is seen to interact with an electric field as opposed to with another charge. To Faraday, the secret to understanding action-at-a-distance is to understand the power of charge-field-charge. A charged object sends its electric field into space, reaching from the "puller to the pullee." Each charge or configuration of charges creates an intricate web of influence in the space surrounding it. While the lines are invisible, the effect is ever so real. So as you practice the exercise of constructing electric field lines around charges or configuration of charges, you are doing more than simply drawing curvy lines. Rather, you are describing the electrified web of space that will draw and repel other charges that enter it. We Would Like to Suggest ... Sometimes it isn't enough to just read about it. You have to interact with it! And that's exactly what you do when you use one of The Physics Classroom's Interactives. We would like to suggest that you combine the reading of this page with the use of our Put the Charge in the Goal Interactive and/or our Electric Field Lines Interactive . Both Interactives can be found in the Physics Interactives section of our website. Both Interactives provide engaging environments for exploring electric field lines. Check Your Understanding Use your understanding to answer the following questions. When finished, click the button to view the answers. 1. Several electric field line patterns are shown in the diagrams below. Which of these patterns are incorrect? _________ Explain what is wrong with all incorrect diagrams. 2. Erin Agin drew the following electric field lines for a configuration of two charges. What did Erin do wrong? Explain. 3. Consider the electric field lines shown in the diagram below. From the diagram, it is apparent that object A is ____ and object B is ____. a. +, + b. -, - c. +, - d. -, + e. insufficient info 4. Consider the electric field lines drawn at the right for a configuration of two charges. Several locations are labeled on the diagram. Rank these locations in order of the electric field strength - from smallest to largest. 5. Use your understanding of electric field lines to identify the charges on the objects in the following configurations. 6. Observe the electric field lines below for various configurations. Rank the objects according to which has the greatest magnitude of electric charge, beginning with the smallest charge.

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This supercomputer simulation shows one of the most violent events in the universe: a pair of neutron stars colliding, merging and forming a black hole. A neutron star is the compressed core left behind when a star born with between eight and 30 times the sun’s mass explodes as a supernova. Neutron stars pack about 1.5 times the mass of the sun — equivalent to about half a million Earths — into a ball just 12 miles (20 km) across. As the simulation begins, we view an unequally matched pair of neutron stars weighing 1.4 and 1.7 solar masses. They are separated by only about 11 miles, slightly less distance than their own diameters. Redder colors show regions of progressively lower density. As the stars spiral toward each other, intense tides begin to deform them, possibly cracking their crusts. Neutron stars possess incredible density, but their surfaces are comparatively thin, with densities about a million times greater than gold. Their interiors crush matter to a much greater degree densities rise by 100 million times in their centers. To begin to imagine such mind-boggling densities, consider that a cubic centimeter of neutron star matter outweighs Mount Everest. By 7 milliseconds, tidal forces overwhelm and shatter the lesser star. Its superdense contents erupt into the system and curl a spiral arm of incredibly hot material. At 13 milliseconds, the more massive star has accumulated too much mass to support it against gravity and collapses, and a new black hole is born. The black hole’s event horizon — its point of no return — is shown by the gray sphere. While most of the matter from both neutron stars will fall into the black hole, some of the less dense, faster moving matter manages to orbit around it, quickly forming a large and rapidly rotating torus. This torus extends for about 124 miles (200 km) and contains the equivalent of 1/5th the mass of our sun. Scientists think neutron star mergers like this produce short gamma-ray bursts (GRBs). Short GRBs last less than two seconds yet unleash as much energy as all the stars in our galaxy produce over one year. The rapidly fading afterglow of these explosions presents a challenge to astronomers. A key element in understanding GRBs is getting instruments on large ground-based telescopes to capture afterglows as soon as possible after the burst. The rapid notification and accurate positions provided by NASA’s Swift mission creates a vibrant synergy with ground-based observatories that has led to dramatically improved understanding of GRBs, especially for short bursts.

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Grade: 4 and up Time: 20-30 minutes Core content: Fossils are evidence of past life. Objectives and summary In this activity, students learn how scientists determine what prehistoric animals looked like based on their bones. The activity reinforces the concept that fossils are mostly the remains of hard parts of ancient life and integrates paleontology with biology. The instructor and students will use the appearance of modern animals to reconstruct what an ancient animal, a Tyrannosaurus rex (T. rex), may have looked like when it was living. The instructor will draw the T. rex on a chalkboard over a projected image of a T. rex skull. You do not need to be an artist to do this activity. Students follow along on their own worksheets. What they will see on the chalkboard is the projected image. At the end of the activity, when the projected image is turned off, all that is left is a drawing of the mighty T. rex! Fossils are evidence of ancient life in rock. Most fossils represent the hard remains of ancient life. In animals with backbones, called vertebrates, bones and teeth are generally the only parts of the animals that are fossilized. Soft tissues, such as skin, muscles, and hair, generally are not preserved, because they rot or are eaten before the animal is fossilized. Any picture of an ancient dinosaur in a book or movie is an artist's illustration of what the ancient creature looked like. Dinosaurs are long extinct. But scientists can determine what dinosaurs looked like based on their fossils. The study of fossils is called paleontology. Paleontologists are the scientists that study fossils. Paleontologists who study dinosaurs, analyze the fossilized dinosaur bones to determine how they fit together. They compare the fossil bones to the bones of animals that live today. Dinosaurs were reptiles. Some were bird like. Others were large like elephants, and big mammals that live today. By studying the way the soft tissues, like muscles and skin, are attached or cover the bones of living animals, paleontologists can interpret how they may have attached or covered the bones of prehistoric animals. In this activity, students will be junior paleontologists. They will reconstruct what the most famous dinosaur, T. rex, looked like based on a T. rex skull and data they collect about modern animals. This is a cast of the T. rex skull, called "Stan." The cast is owned by Walter Gross, of Lexington, who graciously allowed us to use an image of the cast for this educational activity. You will need to make an overhead transparency from a copy of this image, or use a digital image copied to a slide, for the activity. The soft parts of a fossil animal can be inferred based upon comparison of the skull to skulls of modern animals. The locations of muscles in this image are based upon illustrations in Horner and Lessem (1993), and Webster (1999) (see references). If the photograph with soft parts does not copy well, a second image using a drawing of the skull, rather than a photo, can be seen by clicking here. a. The instructor needs to make an image of the T. rex skull provided here. Pdf file formats are provided for easy copying. If the instructor has access to a color copier, the T. rex skull page can be copied on an overhead transparency (make sure the correct kind of transparency sheet is used for your copier. The image can also be saved as a digital file from which a slide can be made at many photographic stores for use in a slide projector. Whichever method the instructor uses, you will need an image that you can project on a chalkboard. b. An image can also be made of the T. rex Soft Parts images (either superimposed on the skull photograph or skull drawing). This may be more detailed than is needed for younger students, but will be interesting to older students who have a better understanding of anatomy. c. Make a copy of the Draw T. rex Worksheet for each student. d. Students should be assigned to look at pictures of large reptiles (such as crocodiles, alligators, iguanas, and komodo dragons), large mammals (such as elephants and rhinos) and large birds (such as emus and ostriches). This can be done the night before as a homework assignment, or it can be a class activity, just prior to drawing T. rex. Tell students to list adjectives that describe the skin of the animals pictured. What does the animal's skin look like (e.g., wrinkled, scaly)? What do the animal's eyes look like? Do the animals have tongues? What colors are the animals (e.g., green, brown)? If the animal's skin have patterns, what kinds are there (e.g., stripes, spots)? 1. Ask the students to define fossils. Most will say bones or dinosaur bones. Stress that fossils are any evidence of ancient life in rocks, not just bones. But bones are fun. Dinosaur bones are even funner. Ask the students, what scientists who study dinosaur bones are called. Define paleontologists. Paleontologists are scientists who study fossils. Tell the students that today they are junior paleontologists, and they are going to draw the king of the dinosaurs, T. rex, but they are going to draw T. rex based on data, a T. rex skull, just as a paleontologist would. 2. Explain to students that dinosaur fossils are mostly just the remains of the hard parts of these ancient animals. Ask them, if they know what parts of a human body are likely to be fossilized? Bones and teeth would be most likely. For younger students, the instructor might point out the fact that there are bones under the skin. If they hold up their hands to a light, they may be able to see their finger bones. Have them tap their teeth. These are hard parts. What are the soft parts of their bodies? Have them pinch and pull up the skin from their wrist. Have the students make a muscle with their arms. Explain that muscles occur beneath the skin and these are not generally preserved as fossils. Other soft parts of the body, like tongues and eyes, can also be pointed out. These are not preserved as fossils, but paleontologists can infer where they would have occurred in ancient animals based on their position in modern animals. 3. Now hand out the Draw T. rex Worksheet to each student. Make sure to tell them not to start yet. Each student will need a pencil. If there is time for students to color their drawings, they can do that in the last step or as a homework assignment. It is easier to draw most of the activity in pencil, so that any mistakes may be erased along the way. 4. Dim the lights in the area in which the chalkboard occurs and project the T. rex skull image on the chalkboard using an overhead projector or slide projector. Explain that the drawing of the skull on the worksheet is a sketch of this photograph. The skull is a cast of a T. rex that was found in South Dakota, and is informally known as "Stan." Explain that paleontologists have to reconstruct the soft parts of Stan from the hard parts found as fossils, like this skull, and knowledge about the soft parts of living animals. If you made an additional image of the T. rex Soft Parts page show it now. The students should not draw the muscles, they will be drawing the exterior appearance of T. rex. Explain that scientists can look at how muscles and skin attach and cover the bones of modern animals and reconstruct how they may have covered ancient animals, like this T. rex. Muscle attachments leave scars on bones. Muscle movement smooths bones beneath. These subtle markings can be preserved on fossil bones, and the placement of muscles can be inferred for the fossil. 5. Ask the students, what part of the body are they looking at when they look at a T. rex skull? The head. Ask what are skull bones covered by? Skin, muscles, and other soft tissues. To draw the skin on the T. rex skull, connect the long-dashed lines on the outside of the jaws on the Draw T. rex Worksheet as shown in the figure. Do not trace the teeth yet, but connect the line at the base of the teeth that outlines the jaws. You can point out that the dashed line at the rear and bottom of the skull does not exactly follow the bones of the skull. The dashes have been drawn in these areas based on the probable position of jaw muscles, that would have been beneath the skin. The trace of the actual jaws is shown by short dashed lines. The instructor needs to demonstrate where to draw, by drawing with chalk on the chalkboard over the projected image of the T. rex skull. The instructor should also walk around the classroom to make sure the students are connecting the correct lines. 6. Next, the instructor should point to the holes in the upper jaw bone of the skull. Explain that in modern animals, holes in the skull are where noses, eyes, and muscles are located. Ask the students, which hole was probably the nose hole? If there is hesitation, ask them to think about the animals they looked at in their picture books. Are noses in the front or rear of most reptile's heads? The front. 7. Now draw the nose. You can ask the students to look at each other. What color is the inside of their neighbor's nose? Dark, or black. Tell students to fill in the nostril hole on their worksheet dark or black. The instructor should fill in the nostril hole on the projected image on the chalkboard. 8. Ask the students, which hole do they think the eye was in? In dinosaurs, the eye hole is generally the third back from the front. It is the narrow hole on the image. Tell the students that in some dinosaur fossils, rings of tiny bones that supported the eyes have been found. The bony rings indicate that the eye occurred in the upper part of the narrow hole, as shown in the figure to the right. Have students look at the eye types on the Draw T. rex Worksheet. Several different types of eyes are shown. Some eyes are football- or saucer-shaped. Some are circular. The illustrations are provided to help students draw eyes. These are all eye shapes that modern reptiles and birds have. The instructor might ask the students if any of the eye shapes provided are similar to the animals they looked at in their picture books. No one eye shape is more right or wrong. Tell the students to draw an eye in the eye hole. The instructor should draw an eye in the eye hole on the projected image on the chalkboard. Then the instructor should walk around the classroom to make sure the students are drawing the eye in the correct position. 9. Next, ask the students what is around their eyes? Eyelids. Most land animals have eyelids. T. rex probably had eyelids. The instructor can draw eyelids around the eyes on the projected image. Tell students to draw U-shapes below the eyes. If you want to make T. rex look mean use heavy shading around the eyes, or make a thick black circle around the eye. 10. Students may ask about the 2nd and 4th holes on the upper skull. Explain that these were areas of muscle attachments. They also served to lighten the skull. Bone is heavy. If the holes were filled with solid bone, as in the rest of the skull, Stan might have had problems getting his head off the ground in the morning. 11. Ask students what should go between the upper and lower jaw? A mouth. Tell students not to draw the mouth just yet. They will draw the mouth in stages. First, show that the teeth have been colored in two colors on the projected image on the chalkboard. The dark part represents parts of the teeth that were worn and exposed to air. The lighter-colored part of the teeth were unworn. Ask the students, are all of their teeth exposed to the air? Is there any part hidden? What hides the bottom of their teeth? Their gums. There is some evidence that T. rex may have had gums. The fossil teeth are worn above the gum line, and smooth beneath it. To draw the gums, the instructor should connect the lines of shading on the teeth (about half way down the teeth on the projected image). On the Draw T. rex Worksheet, the teeth are drawn as solid lines as they would appear above the gums. Students should be told to draw a horizontal line that connects the base of the teeth to form the gums. Dotted lines beneath each tooth, show where the teeth occur beneath the gums. The instructor will want to walk around the classroom to make sure students have connected the correct lines. These do not need to be exact. Teeth are drawn on the Worksheet, but not on the chalkboard. The instructor will need to trace the parts of the teeth that stick out above the gum line on the chalkboard. While drawing, ask the students if some of the smaller teeth on their Worksheet are below the gums? Yes. T. rex lost teeth and had teeth replaced just like the students, but the teeth were bigger and stronger. How much money would the dinosaur tooth fairy have had to leave for one of these teeth! 12. Next, tell the students to open their mouths. From the sides of their face, can the student next to them see all the way back in their mouth? No. Most animals, including modern reptiles have ligaments that attach the jaws together. These ligaments may be covered by skin. This can be shown with pictures of alligators or crocodiles in which the animals have their mouths opened. The instructor should sketch the jaw-connecting ligament at the back of the mouth on the chalkboard image. Tell students to do the same on their Draw T. rex Worksheet. Again, the instructor may want to walk around the room to check that the correct lines are being drawn. 13. What else is in the mouth? A tongue. Tongues, are soft parts. They don't leave any fossil evidence. Noone knows if T. rex had a tongue, or what shape it would have been, but since most large predators and scavengers (birds, mammals, and reptiles) have tongues, you can draw a tongue on T. rex. The instructor should draw a tongue on the projected image. If students don't want to draw a tongue, they don't have to. Also, some animals have small tongues that lay on the bottom of the mouth, and can't always be seen between the teeth when the animal's mouth is open. 14. Now the face of T. rex is mostly complete. Ask the students what is missing? What is reptile skin covered by? Scales. Tell the students that some fossils have been found of dinosaur skin impressions. Most of the impressions show small pebbly scales, somewhat like the pigskin on a football or basketball. Often the skin impressions preserve wrinkling. Birds and big mammals also have bumpy, pebbly or wrinkled skin beneath their feathers or hair. Other fossilized scale impressions show large scales. You might want the students to describe the scales that modern reptiles have. Many reptiles have combinations of different scale patterns, especially around their face. A close-up picture of an iguana can be used as an example. Have the students look at the choices of scale patterns they are provided with on the Draw T. rex Worksheet. The instructor may want to draw each type on different parts of the projected image on the chalkboard to show students how they are drawn. Simple patterns have been chosen to make this step easy. Stress that no one scale pattern is more correct than another. Tell the students to be creative. They can model the scale pattern after a living animal from the books they've looked at, or use their imagination. The instructor and students should now cover their T. rex head with scales. This will take approximately 5 to 10 minutes. 15. When the instructor is drawing scales, they may point out that some modern reptiles have patterns on their skin. These can be patterns of scales, or patterns of colors across scales. Ask students what patterns they may have seen on modern reptiles in picture books. Many modern animals have patterns in order to blend in with their environment. This is called camouflage. Stripes help to camouflage animals in areas of tall, straight plants. Spots and blotches help camouflage animals in shrubby or leafy areas. Both predators and prey use camouflage. Large animals often have no patterns. The instructor may want to use an elephant as an example. Uniform color helps elephants with heat control. Large birds like emus and ostriches also tend to be uniform in color. This may also have been the case with large dinosaurs. Uniform color in large modern animals also can result from large animals brushing and scraping into plants, rocks, and trees much of their life. Uniform color can also be a type of camouflage. Lions are uniformly tan in color, which helps them blend in with the tan grasses of the African Savannah. Tell students they can draw patterns on their T. rex, or not, its up to them. There is no right or wrong answer. You could also add some feathers to the back of your T-rex drawing. Although it may seem strange, theropod dinosaurs like T-rex are very closely related to birds. In fact, fossils of cousins of T-rex have been found which were covered with feathers. Feathers are not easily fossilized, but several recent fossil discoveries in China with exceptional preservation of fossil details, indicate that smaller and older ancestors of tyrannosaurs were covered with feathers. Some theropod dinosaurs had downy feathers covering their bodies or parts of their bodies. Some smaller theropods, for example the droemaeosaurs (commonly called "raptors"), also had longer feathers protruding from their arms, legs, and tails. They weren’t birds, just dinosaurs with feathers! So far, no T-rex fossils have ever been found with feathers. Feathers, however, are not commonly preserved, and T-rex is very closely related to dinosaurs that had feathers, so it’s possible that T-rex was covered with feathers. 16. This activity can be done in black and white or color. If you want to use color, ask students, what colors they saw in modern reptiles and other large animals? Grays, greens, and browns are most common in modern reptiles. Large animals also tend to be gray and brown. But birds can be very colorful. There is mounting evidence that birds are related to dinosaurs. In fact, in a National Geographic article (v. 196, no. 5, p. 98-99) on feathered dinosaurs, C. Sloan (1999) paints T. rex hatchlings with feathers. Some dinosaurs may have been colorful. Bright colors are used in many animals to attract a mate (boyfriend or girlfriend). Again, students can be creative. Students can color their T. rex in the classroom, or if time is running out, they can color them at home. 17. Now the instructor should turn off the projected image, which generally is brighter than the drawing the instructor made. When the projected image is turned off, what remains on the chalkboard (like magic) is a drawing of T. rex. This may be greeted with gasps and exclamations. Explain that they all started with just the hard parts, and based on what they know about modern animals, have reconstructed what Tyrannosaurus rex looked like in life. Have the students compare their pictures. Do they all look the same? No. Yet they all started off with the same data, the hard parts, or skull of a T. rex. Differences occurred because of the different ways each student reconstructed the soft parts. This is one of the reasons pictures of ancient animals in picture books often look different. For more information on Tyrannosaurus rex in books: For more information on Tyrannosaurus rex on the Internet:

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In the last section, we saw that a flash circuit needs to turn a battery's low voltage into a high voltage in order to light up a xenon tube. There are dozens of ways to arrange this sort of step-up circuit, but most configurations contain the same basic elements. All of these components are explained in other HowStuffWorks articles: - Capacitors - Devices that store energy by collecting charge on plates (see How Capacitors Work) - Inductors - Coiled lengths of wire that store up energy by generating magnetic fields (see How Inductors Work) - Diodes - Semiconductor devices that let current flow freely in only one direction (see How Semiconductors Work) - Transistors - Semiconductor devices that can act as electrically controlled switches or amplifiers (see How Amplifiers Work) The diagram below shows how all of these elements come together in a basic flash circuit. Taken in its entirety, this diagram may seem a little overwhelming, but if we break it down into its component parts, it isn't that complicated. Let's start with the heart of the circuit, the main transformer, the device that actually boosts the voltage. The transformer consists of two inductors in close proximity to each other (for example, one might be wound around the other, with both might be wound around an iron core). If you've read How Electromagnets Work, you know that passing current through a coiled length of wire will generate a magnetic field. If you've read How Inductors Work, you know that a fluctuating magnetic field, generated by fluctuating electric current, will cause a voltage change in a conductor. The basic idea of a transformer is to run current through one inductor (the primary coil) to magnetize another conductor (the secondary coil), causing a change in voltage in the second coil. If you vary the size of the two inductors -- the number of loops in each coil -- you can boost (or reduce) voltage from the primary to the secondary. In a step-up transformer like the one in the flash circuit, the secondary coil has many more loops than the primary coil. As a result, the magnetic field and (by extension) voltage are greater in the secondary coil than in the primary coil. The trade-off is that the secondary coil has weaker current than the primary coil. (Check out this site for more information.) To boost voltage in this way, you need a fluctuating current, like the AC current (alternating current) in your house. But a battery puts out constant DC current (direct current), which does not fluctuate. The inductor's magnetic field only changes when DC current initially passes through it. In the next section, we'll find out how the flash circuit handles this problem.

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Write a step-by-step plan of your lesson. Look at the example plan (p7) in module 11 and note the staging. Stage 1. Activity. Interaction. Timing. Stage 2. Activity. Interaction. Timing. Answer: Warm-up: What am I? The warm-up starts by me saying “what am I?” and I begin describing the kind of animal I am. Students will raise their hands when they think they know what I am. S-S, T-S: 5 minutes Introduction: Announce the game of “Dinosaur Danger!" to be played later in the lesson. Ask if the students know the game. T-S: 1 minute Drilling: Using flashcards I ask a question or make a statement and elicit answers. Examples: What is this? This is a cat. How many pigs are there in the pen? There are three pigs in the pen. What do you see? A fish swimming in the river. What does a monkey love to eat? They love to eat a banana. Does a cat drink milk? YES! It does. What does the rabbit eat? The rabbit eats a carrot. Can a bird swim? NO! It can’t. What does a bird do? It flies in the air. T-S, S-T, 6 minutes Plenary: Odd one out The students are provided with a set of three statements. Students should decide which is the odd one out and why. They must also be prepared to justify their choice. T-S, S-T: 2 minutes Lead-in to the game: Explain the rules of the game of “Dinosaur Danger!". Check understanding. Demonstrate: I will hold up a flashcards, students come up with a sentence for the picture. Example: Flashcard (Girl with a dog) “She has a dog.” But be careful of the dinosaur card, the students have to rush to opposite side of the classroom and touch the wall before I can touch the wall where they were previously standing. T-S: 2 minutes Game: The class gather’s at one side of the classroom. I hold up a flashcard and the students have to make a sentence out of it using indefinite articles and basic structures. Example: That’s a bear But when they see the dinosaur card the students have to rush to the opposite side of classroom and touch the wall. As the students rush to the opposite side I have to touch the wall at the side where they were previously standing. If any of the students take longer than me to touch their wall, they are out. (But you rarely need to enforce this rule as the students will just enjoy the rushing to touch the wall on the opposite side.) T-S 8 minutes Follow-up Activity: Fly swatter Place words on wall/board. Divide class into relay teams for a relay race. Give a clue “I like to eat a banana”. The student in front of each line goes to the word wall/board and swats the correct animal. T-S, S-T 5 minutes Homework: Students will write a short paragraph about their favorite animal and why. T-S 1minute Comments and what to fix above submitted work: This is a good attempt; however I'd like you to resubmit: You need to think of a game to practice vocabulary of animals in one of the mentioned structures e.g. 'They are cats' or 'I have a dog' - Remember - your students only know basic structures: “This is a…”, “These are…”, “I can see…”, “I have…”, and personal pronouns. - Have a look at the example given in the task guidelines to help you with the stages. Note the game is introduced in stage 8. Students need to practice vocabulary of animals and the structures they need for the game in the stages leading up to stage 8. Please resubmit. You need to add the game – you don’t need to change all of your submission. When adding a game make sure that your students adequately prepare for it, that is practices the target structures/vocab, and that it is fun! We don't correct assignments.

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Here's the musical way to learn about nouns, verbs, and pronouns. These songs help boost the skills needed for improved reading comprehension and writing. Cool songs and rhymes make grammar rules easy to remember. Students follow along with the book and practice identifying parts of speech in sentences. Immediate feedback by the performers allows kids to check their progress. Ages 8 & up. Approx. 35 minutes. Music is a fun and effective way to learn the rules about nouns, verbs, and pronouns. A reproducible activity book allows kids to follow along with the songs and join the fun. The booklet also includes worksheets for pronouns, linking verbs, and verb tense. Plus, additional activities provide practice identifying parts of speech in sentences. Teachers and parents have permission to photocopy the pages for instructional use. Grammar song titles include: "These are audios with a difference: original tunes with attention-grabbing lyrics which teach kids. Grammar is available for grades 1 – 5 and provides a variety of entertainers who put together a CD/book program imparting basic grammar concepts. Educators working with pop musicians produce fine blends of education and entertainment." – Children's Bookwatch "Learning with a beat is the theme of this well done selection. [The CD features] upbeat, contemporary musical songs with clear understandable vocals and lots of repetition for skills retention. Grammar uses musical numbers to introduce the parts of speech, which students then have to identify during musical pauses. – Booklist

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Related Information Links Units, Dimensions, and Conversions SI units (cubic meters and K). When measuring a quantity, the units we use are just as important as the numerical value we obtain. Stating that the mass of an object is one (1) says very little about the actual mass of the object. It is perfectly reasonable for an instructor to respond to such an answer: "One what???" So, what are the basic units of measurement? Let's start with a list of some things we might measure: Each of these quantities has a variety of units we might use. Here are a few examples. The units in bold font are the base units used in the SI System of Units the recommended scientific system of units. In addition to length, mass, time and temperature, the list of base quantities includes three others you may not have seen before: electric current (ampere), luminous intensity (candela) and amount of a chemical substance (mole). The last unit (mole) is constantly used in chemistry and explained on the stoichiometry page. So, what do you need to know? When studying chemistry you will measure many quantities with units that are actually combinations of the base units. Be sure to include the units in your notes when you encounter a new term. Here is a list of quantities that you should already be familiar with from previous classes. Follow the link to a short description for those you don't recall. The factors of all the prefixes are easier represented in scientific notation. For example, kilo denotes a factor of 1000. In scientific notation this would be As you might notice, factors with a positive exponent move the decimal to the right, making a factor greater than one. Numbers with a negative exponent move the decimal to the left, making a number less than one. For example, kilo- represents multiple of a thousand, and milli- represents muliples of a thousandth, so milli- = 0.001 = 10-3 Here are examples of other prefixes with their names, symbols, and factors: Changing between units is easy if we have a conversion equation. For example, Robert Millikan (a 20th century physicist) performed a landmark experiment with x-rays and determined the mass of an electron to be 9.1x10-31 kg. While this is the standard way to represent this quantity, it would also be correct to use grams (g) or milligrams (mg): How do we change between units like this? Here are two conversion equations that will help in this situation: 1 g = 1000 mg Notice that we can rearrange these equations in several ways dividing by one of the sides: We have formed several ratios which are all equal to 1! Now we need to remember a crucial fact from arithmetic: This is the key to changing units! Consider changing from kg to g. Which ratio equal to 1 should we multiply kilograms by to get grams? Well, if we use the fraction with grams on top and kilograms on bottom, kilograms will "cancel out" when we simplify. Watch: Notice that we multiplied numbers in scientific notation. We can use the EE button on a calculator as follows: The calculator displays: If you are still unsure about how to handle scientific notation on your calculator see the section on Calculator Fundamentals. Changing from kilograms to milligrams works in the same way, except we need to convert from kg to g and then from g to mg since we aren't given a single kg-to-mg conversion equation. We can combine these into one step, though! Watch: We just multiplied by "one" twice, choosing the ratios that allowed us to cancel out the kg and the g units. So what other conversion equations are there? Click here to look at the ones from your chemistry text. How many should you know without checking the list? Fair question! Ask your instructor. Try It Out [Numbers and their Properties] [Numbers in Science] [Ratios and Proportions] [Units, Dimensions, and Conversions] [Percents] [Simple Statistics] [Logarithms] Copyright © 1996-2008 Shodor Please direct questions and comments about this page to

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ALGEBRA IS A METHOD OF WRITTEN CALCULATIONS that help us reason about numbers. At the very outset, the student should realize that algebra is a skill. And like any skill -- driving a car, baking cookies, playing the guitar -- it requires practice. A lot of practice. Written practice. That said, let us begin. The first thing to note is that in algebra we use letters as well as numbers. But the letters represent numbers. We imitate the rules of arithmetic with letters, because we mean that the rule will be true for any numbers. Here, for example, is the rule for adding fractions: The letters a and b mean: The numbers that are in the numerators. The letter c means: The number in the denominator. The rule means: "Whatever those numbers are, add the numerators Algebra is telling us how to do any problem that looks like that. That is one reason why we use letters. (The symbols for numbers, after all, are nothing but written marks. And so are letters As the student will see, algebra depends only on the patterns that the symbols make.) The numbers are the numerical symbols, while the letters are called literal symbols. Question 1. What are the four operations of arithmetic, and what are their operation signs? To see the answer, pass your mouse over the colored area. 3) Multiplication: a· b. Read a· b as "a times b." The multiplication sign in algebra is a centered dot. We do not use the multiplication cross ×, because we do not want to confuse it with the letter x. And so if a represents 2, and b represents 5, then a· b = 2· 5 = 10. "2 times 5 equals 10." Do not confuse the centered dot -- 2·5, which in the United States means multiplication -- with the decimal point: 2.5. However, we often omit the multiplication dot and simply write ab. Read "a, b." In other words, when there is no operation sign between two letters, or between a letter and a number, it always means multiplication. 2x means 2 times x. In algebra, we use the horizontal division bar. If a represents 10, for example and b represents 2, then "10 divided by 2 is 5." Note: In algebra we call a + b a "sum" even though we do not name an answer. As the student will see, we name something in algebra simply by how it looks. In fact, you will see that you do algebra with your eyes, and then what you write on the paper, follows. This sign = of course is the equal sign, and we read this -- a = b -- as "a equals (or is equal to) b." That means that the number on the left that a represents, is equal to the number on the right that b represents. If we write a + b = c, and if a represents 5, and b represents 6, then c must represent 11. Question 2. What is the function of parentheses () in algebra? 3 + (4 + 5) 3(4 + 5) Parentheses signify that we should treat what they enclose 3 + (4 + 5) = 3 + 9 = 12. 3(4 + 5) = 3· 9 = 27. Note: When there is no operation sign between 3 and (4 + 5), it means multiplication. Problem 1. In algebra, how do we write a) 5 times 6? 5· 6 b) x times y? xy d) x plus 5 plus x minus 2? (x + 5) + (x − 2) e) x plus 5 times x minus 2? (x + 5)(x − 2) Problem 2. Distinguish the following: a) 8 − (3 + 2) b) 8 − 3 + 2 a) 8 − (3 + 2) = 8 − 5 = 3. b) 8 − 3 + 2 = 5 + 2 = 7. In a), we treat 3 + 2 as one number. In b), we do not. We are to first subtract 3 and then add 2. (But see the order of operations below.) There is a common misconception that parentheses always signify multiplication. In Lesson 3, in fact, we will see that we use parentheses to separate the operation sign from the algebraic sign. 8 + (−2). Question 3. Terms versus factors. When numbers are added or subtracted, they are called terms. When numbers are multiplied, they are called factors. Here is a sum of four terms: a − b + c − d. In algebra we speak of a "sum" of terms, even though there are subtractions. In other words, anything that looks like what you see above, we call a sum. Here is a product of four factors: abcd. The word factor always signifies multiplication. And again, we speak of the "product" abcd, even though we do not name an answer. Problem 3. In the following expression, how many terms are there? And each term has how many factors? 2a + 4ab + 5a(b + c) There are three terms. 2a is the first term. It has two factors: Powers and exponents When all the factors are equal -- 2· 2· 2· 2 -- we call the product a power of that factor. Thus, a· a is called the second power of a, or "a squared." a· a· a is the third power of a, or "a cubed." aaaa is a to the fourth power, and so on. We say that a itself is the first power of a. Now, rather than write aaaa, we write a just once and place a small 4: a4 ("a to the 4th") That small 4 is called an exponent. It indicates the number of times to repeat a as a factor. 83 ("8 to the third power" or simply "8 to the third") means 8· 8· 8. Problem 4. Name the first five powers of 2. 2, 4, 8, 16, 32. Problem 5. Read, then calculate each of the following. a) 52 "5 to the second power" or "5 squared" = 25. b) 23 "2 to the third power" or "2 cubed" = 8. c) 104 "10 to the fourth" = 10,000. d) 121 "12 to the first" = 12. However, it is the style in algebra not to write the exponent 1. a = a1 =1a. The student must take care not to confuse 3a, which means 3 times a, with a3, which means a times a times a. Question 4. When there are several operations, 8 + 4(2 + 3)2 − 7, what is the order of operations? Before answering, let us note that since skill in science is the reason students are required to learn algebra; and since orders of operations appear only in certain forms, then in these pages we present only those forms that the student is ever likely to encounter in the actual practice of algebra. The division sign ÷ is never used in scientific formulas, only the division bar. And the multiplication cross × is used only in scientific notation -- therefore the student will never see the following: 3 + 6 × (5 + 3) ÷ 3 − 8. Such a problem would be purely academic, which is to say, it is an exercise for its own sake, and is of no practical value. It leads nowhere. The order of operations is as follows: In Examples 1 and 2 below, we will see in what sense we may add or subtract. And in Example 3 we will encounter multiply or divide. Note: To "evaluate" means to name and write a number. Example 1. 8 + 4(2 + 3)2 − 7 First, we will evaluate the parentheses, that is, we will replace 2 + 3 with 5: = 8 + 4· 52 − 7 Since there is now just one number, 5, it is not necessary to write parentheses. Notice that we transformed one element, the parentheses, and rewrote all the rest. Next, evaluate the exponents: = 8 + 4· 25 − 7 = 8 + 100 − 7 Finally, add or subtract, it will not matter. If we add first: = 108 − 7 = 101. While if we subtract first: 8 + 100 − 7 = 8 + 93 = 101. Example 2. 100 − 60 + 3. 100 − 60 + 3 does not mean 100 − 63. Only if there were parentheses -- 100 − (60 + 3) -- could we treat 60 + 3 as one number. In the absence of parentheses, the problem means to subtract 60 from 100, then add 3: 100 − 60 + 3 = 40 + 3 = 43. In fact, it will not matter whether we add first or subtract first, 100 − 60 + 3 = 103 − 60 = 43. When we come to signed numbers, we will see that 100 − 60 + 3 = 100 + (−60) + 3. The order in which we "add" those will not matter. There are no parentheses to evaluate and no exponents. Next in the order is multiply or divide. We may do either -- we will get the same answer. But it is usually more skillful to divide first, because we will then have smaller numbers to multiply. Therefore, we will first divide 35 by 5: Example 4. ½(3 + 4)12 = ½· 7· 12. The order of factors does not matter: abc = bac = cab, and so on. Therefore we may first do ½· 12. That is, we may first divide 12 by 2: ½· 7· 12 = 7· 6 = 42. In any problem with the division bar, before we can divide we must evaluate the top and bottom according to the order of operations. In other words, we must interpret the top and bottom as being in parentheses. Now we proceed as usual and evaluate the parentheses first. The answer is 4. Problem 6. Evaluate each of the following according to the order of operations. Question 5. What do we mean by the value of a letter? The value of a letter is a number. It is the number that will replace the letter when we do the order of operations. Question 6. What does it mean to evaluate an expression? It means to replace each letter with its value, and then do the order of operations. Example 6. Let x = 10, y = 4, z = 2. Evaluate the following. In each case, copy the pattern. Copy the + signs and copy the parentheses ( ). When you come to x, replace it with 10. When you come to y, replace it with 4. And when you come to z, replace it with 2. Problem 7. Let x = 10, y = 4, z = 2, and evaluate the following. g) x2 − y2 + 3z2 = 100 − 16 + 3· 4 = 100 − 16 + 12 = 84 + 12 =96. Again, 100 − 16 + 12 does not mean 100 − (16 + 12). That is 168 divided by 100. See Lesson 4 of Arithmetic, Question 4. Question 7. Why is a literal symbol -- x, y, z -- called a variable? Because its value may vary. A variable, such as x, is a kind of blank or empty symbol. It is therefore available to take any value we might give it: a positive number or, as we shall see, a negative number; a whole number or a fraction. Numerical symbols -- 2, 3, 4 -- are called constants. The value of those symbols does not vary. Problem 8. Two variables. Let the value of the variable y depend y = 2x + 4. Calculate the value of y that corresponds to each value of x: When x = 0, y = 2· 0 + 4 = 0 + 4 = 4. When x = 1, y = 2· 1 + 4 = 2 + 4 = 6. When x = 2, y = 2· 2 + 4 = 4 + 4 = 8. When x = 3, y = 2· 3 + 4 = 6 + 4 = 10. When x = 4, y = 2· 4 + 4 = 8 + 4 = 12. Real problems in science or in business occur in ordinary language. To do such problems, we typically have to translate them into algebraic language. Problem 9. Write an algebraic expression that will symbolize each of the following. a) Six times a certain number. 6n, or 6x, or 6m. Any letter will do. b) Six more than a certain number. x + 6 c) Six less than a certain number. x − 6 d) Six minus a certain number. 6 − x e) A number repeated as a factor three times. x· x· x = x3 f) A number repeated as a term three times. x + x + x g) The sum of three consecutive whole numbers. The idea, for example, h) Eight less than twice a certain number. 2x − 8 i) One more than three times a certain number. 3x + 1 Now an algebraic expression is not a sentence, it does not have a verb, which is typically the equal sign = . An algebraic statement has an equal sign. Problem 10. Write each statement algebraically. a) The sum of two numbers is twenty. x + y = 20. b) The difference of two numbers is twenty. x − y = 20. c) The product of two numbers is twenty. xy = 20. d) Twice the product of two numbers is twenty. 2xy = 20. e) The quotient of two numbers is equal to the sum of those numbers. A formula is an algebraic rule for evaluating some quantity. A formula is a statement. Example 7. Here is the formula for the area A of a rectangle whose base is b and whose height is h. A = bh. "The area of a rectangle is equal to the base times the height." And here is the formula for its perimeter P -- that is, its boundary: P = 2b + 2h. "The perimeter of a rectangle is equal to two times the base For, in a rectangle the opposite sides are equal. Problem 11. Evaluate the formulas for A and P when b = 10 in, and h = 6 in. A = bh = 10· 6 = 60 in2. P = 2b + 2h = 2· 10 + 2· 6 = 20 + 12 = 32 in. Problem 12. The area A of trapezoid is given by this formula, A = ½(a + b)h. Find A when a = 2 cm, b = 5 cm, and h = 4 cm. A = ½(2 + 5)4 = ½· 7· 4 = 7· 2 = 14 cm2. When 1 cm is the unit of length, then 1 cm² ("1 square centimeter") is the unit of area. Problem 13. The formula for changing temperature in degrees Fahrenheit (F) to degrees Celsius (C) is given by this formula: Find C if F = 68°. Replace F with 68: "One ninth of 36 is 4. So five ninths is five times 4: 20." Please make a donation to keep TheMathPage online. Copyright © 2015 Lawrence Spector Questions or comments?

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Old data can hold new information when viewed with a fresh pair of eyes. Researchers have used data originally collected during the Apollo missions to the Moon to get a picture of its interior that was previously unavailable. (Note of interest: this isn't the first time in recent memory that data originally collected during the Moon landings has appeared in modern articles.) During the late 1960s and early 1970s, the Apollo astronauts placed four seismometers on the side of the Moon that faces the Earth (the Apollo Passive Seismic Experiment). These instruments continuously recorded the motion of the lunar surface in three orthogonal dimensions until late 1977. Given the small number of listening stations, limited geographical range spanned by the stations, and weak signals emanating from moonquakes, scientists at the time were not able to learn much about the deep interior of the Moon. Using a modern analysis method known as array-processing, scientists were able to combine a series of small amplitude signals from the original data to identify reflections at different layers of the lunar interior. Analysis of these now-visible wave reflections revealed the Moon's inner structure. The data shows that there's a solid inner core with a radius of 240±10 km, a fluid outer core that extended to 330±20 km, and a partially molten boundary area that spread out to 480±15 km. Further than that, and you're in the lunar mantle. One interpretation of the data is that the deepest interior regions of the Moon have similar structure to the inner regions of the Earth. Coupling the measurements and assumptions with phase diagrams of iron-sulfur alloys suggests that the lunar core is approximately six percent sulfur by weight. That's relatively low, and the authors think that we can blame the moon's formation in a major impact event. The depletion of light elements is a "natural consequence of the lunar formation process, through high-temperature devolatilization during the Moon-forming impact: in effect, the present lunar core is likely comprised of thermally processed material from the core of the impactor." ScienceExpress, 2010. DOI: 10.1126/science.1199375

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When looking at a line segment, there is only one line that will pass through the midpoint that will be a constant distance between the two endpoints. This line is called the perpendicular bisector. To construct the perpendicular bisector, we first find the midpoint of the line segment and then use a compass and straightedge to draw the perpendicular line. Sample Problems (2) Need help with "Constructing the Perpendicular Bisector" problems? Watch expert teachers solve similar problems to develop your skills.

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Setting Learning Outcomes Learning outcomes are measurable statements that articulate what students should know, be able to do, or value as a result of taking a course or completing a program. Learning outcomes often take this form: As a result of participating in (program/course name), you (students) will be able to (Action verb) (Learning statement). Students will be able to describe the key characteristics of the different classes of planets. Students will be able to explain economic institutions, such as the Federal Reserve and stock markets. Looking at the previous sample learning outcomes, imagine what course lectures might entail, what learning activities might be effective, and how student learning might be measured. Use learning outcomes as a tool; let them inform your choice of teaching strategies, course activities and assessments. Setting learning outcomes will make it easier for instructors to: - Make hard decisions about selecting course content. - Design assessments that allow students to demonstrate their knowledge and skills. - Design teaching strategies or learning activities that will help students develop their knowledge and skills. - Measure student learning accurately and effectively. Having access to articulated learning outcomes (in a syllabus, for example) helps students: - Decide if the course is a good fit for their academic trajectory. - Identify what they need to do to be successful in the course. - Take ownership of how their progress. - Be mindful of what they are learning. - Ask yourself: what are the most important things a student should know (cognitive), be able to do (skills), or value (affective) after completing the course/program? - Consult a list of action verbs, which are verbs that result in overt behavior or products that can be observed and measured. Bloom's Taxonomy of Educational Objectives provides some useful verbs to write objectives for different levels of learning. See An Introduction to Bloom's Taxonomy from the University of West Florida. - Avoid verbs that are unclear and cannot be observed and measured easily, for example: appreciate, become aware of, become familiar with, know, learn, and understand. - Draft a list of possible learning outcomes. Be realistic in considering what is possible for students to accomplish in your course. Only keep the most essential learning outcomes. - Edit and review the outcomes using the Learning Outcome Review Checklist . Setting learning outcomes is the first step in a five-part process (Walvoord, 2010): - Outcomes: What do we want students to be able to do after the course? - Identify: Where in the curriculum are the outcomes addressed? - Measures: How well are students achieving the outcomes? - Revision: What changes can be made to the course to improve student achievement? - Re-measure: Did the revision to the curriculum work? CTE Setting Learning Outcomes (CU NetID required to access. Link redirects to login page.) Learning Outcomes Checklist Working Session on Learning Outcomes and Assessments Past CTE Presentation Materials Bloom, B. S. (1956). Taxonomy of educational objectives: The classification of educational goals. New York: Longmans, Green. Walvoord, B. E. (2010). Assessment clear and simple: A practical guide for institutions, departments and general education. San Francisco: Jossey-Bass.

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In the period immediately following the Big Bang, all matter was hot. An explosive cloud of light and elementary particles moved outward and, after the first few hundred thousand years, began to cool. This is mostly a product of the spreading out of matter, and as the universe expanded the matter that made it up cooled further and further. This process was accompanied by the release of intense radiation in the microwave range, and much of that radiation is still hurtling through space. When it falls on Earth we can collect it, and a full accounting of the so-called Cosmic Microwave Background Radiation (CMBR) can give us a snapshot of what the universe looked like in those early aeons of cooling. The South Pole Telescope, which collects this information, is aptly named. It was placed at one of Earth’s coldest extremes to avoid water vapor in the air; only Antarctica’s dry atmosphere will allow enough of the roughly 2 millimeter radiation to reach the collector. The dish itself is more than 30 feet across, bouncing microwaves to a camera built from the ground for this telescope’s research team. The detector is built around a superconducting thin film which loses superconductivity when heated. Even just the impact of a CMB ray imparts enough heat to cause a noticable change in conductivity. The CMBR has actually been mapped several times already by projects like the Cosmic Background Explorer, or COBE, and is now known in exquisite detail. What the South Pole Telescope does is look at this information to answer much more modern and specific questions than ever before. Specifically, what can the state of the early universe tell us about dark matter and dark energy? They’re hoping, quite a lot. Very little concrete information is known about these two quantities, which together are estimated to comprise 95% of the universe. But one thing that is known is dark energy can affect the formation of galaxy clusters and super-clusters. These mega-features of the universe have shifted the path of the CMBR rays as they have traveled these past several billion years. By studying the characteristic shift in the microwave radiation signature, these researchers hope to be able to infer something about the dark energy that caused it.

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High School: Algebra Arithmetic with Polynomials and Rational Expressions HSA-APR.C.5 5. Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle. The Binomial Theorem and Pascal's Triangle are very important concepts for two reasons. First, they're capitalized, and when words are capitalized, you know they're a big deal. Second, both the Binomial Theorem and Pascal's Triangle make expanding polynomials way easier. Students should be able to expand (x + y)n using Pascal's Triangle, where x and y can be anything. Pascal's Triangle provides the coefficients for the expansion, and the Binomial Theorem explains Pascal's Triangle. They go together like ramma lamma lamma ke ding a de dinga dong…whatever that means. The Binomial Theorem can be explained using combinations, usually because they're the easiest to visualize and explain. For example, flipping a coin is a classic example since there are two sides. How many combinations are possible with 1 heads and 2 tails? We could have HTT, THT, and TTH. There are three possible combinations. We can assign values to our total number of trials (n = 3) and our total number of desired outcome (heads, for example, would be k = 1). The notation nCk is a way of saying, "The number of different combinations we can have if, out of n trials, our desired outcome occurs k times." For example, we can use nCk if we flip a coin n times and we want to know how many different ways we can have k heads (or k tails, whichever we want). We can calculate nCk using the formula Those exclamation points aren't just because we're excited about n and k. They're mathspeak for "factorial," which translates to n × (n – 1) × (n – 2) × … × 2 × 1. But you can be excited about n and k too. In our example of three coin flips (n = 3) and 1 heads (k = 1), this equals There are 3 possible ways to get 1 heads out of 3 coin flips. We can use this same logic when expanding (x + y)n. How many ways can we get 3 x's and 2 y's, for example? (Note that there are the same number of ways to get 2 x's and 3 y's.) This can be written as 5C3, which equals Let's now think about all ways of getting k x's and (n – k) y's out of n outcomes. When n = 0, we can have 0C0, which equals 1. Our values for n = 2 are 1C0 and 1C1, both of which equal 1 as well. For n = 2, 2C0 and 2C2 equal 1, but 2C1 equals 2. Students should know that continuing with these calculations would get us Pascal's Triangle, in which each number is the sum of the two numbers above it. Let's use Pascal's Triangle to expand (x + y)5. (x + y)5 = x5 + 5x4y + 10x3y2 + 10x2y3 + 5xy4 + y5 The coefficients of each term correspond to the row of Pascal's Triangle in which n = 5. The exponents of the x's start from n and decrease to 0, while the orders of the y's start at 0 and increase until we get to n. Pretty awesome, right?

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Help clear up the pronoun confusion by having your third grader practice replacing sentence subjects with the pronouns that go with them. Young writers get a chance to practice finding just the right adjective to place in each sentence. Check out this worksheet to help your third grader practice subject verb agreement. Learning plural nouns is a challenge! If your child is having trouble remembering the plural forms of different nouns, this worksheet is key. Let your third grader test her spelling skills by filling in the blanks to complete the words given. Then have her place them in alphabetical order. This worksheet will give your child the practice he needs to identify sentence fragments and rewrite them as complete sentences. Possessive nouns worksheets give kids lots of grammar practice. This possessive nouns worksheet will teach your child how to make a singular possessive noun. Get your third grader on board with the parts of a sentence with this worksheet that helps her practice identifying the subject and predicate of a sentence. Boost grammar knowledge with this great worksheet that's all about possessive pronouns. Boost your third grader's pronoun savvy with an exercise in replacing objects with their pronouns.

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view a plan High School: Introduction to Geometry Proofs Common Core, Math 9, 10, 11 Students will discuss knowledge and research about triangles and prove a theorem about triangles. CCSS.Math.Content.HSG-SRT.B.4 Prove theorems about triangles. Students will understand what a theorem is and how theorems are used in math. Students will prove one theorem about triangles. Computers and materials for research (consider setting up a Google search with web sites that you want students to use) Large chart paper Do Now: Journal Entry and Discussion (5 minutes) Ask students to write silently for two minutes and then discuss: How do you know something is true in math? Research (20 minutes) Tell students that in geometry, mathematicians create theorems, or statements that are proven based on previous theorems and ideas. In geometry, we write proofs to use knowledge and concepts to prove theorems. We are going to start our study of geometry proofs with the study of triangles. Divide students into groups to use Internet and other resources to research triangles. Have students research the questions: What do we know about triangles? What is always true about triangles? Provide students with 15 minutes to research. Students should cite their sources and references for each piece of information that they find. Research Review and Synthesis (10 minutes) As a whole group, compile the information that you found. In addition, compile a list of web sites that provide good references for math. Guided Practice (15 minutes) Based on the information that students find. Create a geometry proof for a core triangle concept or problem (for example, prove the Pythagorean theorem or prove the area of a triangle). Math Talk (5 minutes) Ask students to revisit their journal entry from the beginning of class and add to their answer. Then, as a class, discuss: Why is it important to prove what we know in math? How does the organization of a proof help communicate ideas?

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From This Story Despite claims in the 1890s that Mars was filled with canals teeming with water, research over the past several decades has suggested that in fact, Mars has only a tiny amount of water, mostly near its surface. Then, during the 1970s, as part of NASA’s Mariner space orbiter program, dry river beds and canyons on Mars were discovered—the first indications that surface water may have once existed there. The Viking program subsequently found enormous river valleys on the planet, and in 2003 it was announced that the Mars Odyssey spacecraft had actually detected minute quantities of liquid water on and just below the surface, which was later confirmed by the Phoenix lander. Now, according to an article published yesterday in the journal Geology, there is evidence that Mars is home to vast reservoirs of water in its interior as well. The finding has weighty implications for our understanding of the geology of Mars, for hopes that the planet may have at some point in the past been home to extraterrestrial life and for the long-term prospects of human colonization there. “There has been substantial evidence for the presence of liquid water at the Martian surface for some time,” said Erik Hauri, one of the study’s authors. “So it’s been puzzling why previous estimates for the planet’s interior have been so dry. This new research makes sense.” The research team, led by led by University of New Mexico scientist Francis McCubbin, didn’t even have to go all the way to Mars to find the water—they just closely looked at a pair of meteorites we’ve already had for some time. The Shergotty meteorite, which crashed in Bihar, India in 1865, and the Queen Alexandria Range 94201 meteorite, which landed in Antarctica and was discovered in 1994, were both ejected from Mars roughly 2.5 million years ago. Because they formed due to volcanic activity, when molten Martian mantle was brought to the surface and crystallized, they can tell us a great deal about the planet’s insides. “We analyzed two meteorites that had very different processing histories,” Hauri said. “One had undergone considerable mixing with other elements during its formation, while the other had not.” For both of the meteorites, the team looked specifically at the amount of water molecules locked inside crystals of the mineral apatite and used this as a proxy for how much water was contained in the original rock on Mars that produced the meteorites. To determine the precise amount of water, they used a technology called secondary ion mass spectrometry, which shoots a focused beam of ions at the sample and measures the amount of ions that bounce off of the surface. The amount of water in the meteorites suggested that the Martian mantle contains somewhere between 70 and 300 parts per million of water—an amount strikingly similar to Earth’s own mantle. Because both the samples contained roughly the same water content despite their different geological histories on Mars, the researchers believe that the planet incorporated this water long ago, during the early stages of its formation. The paper also provides us with an answer for how underground water may have made its way to the Martian surface: volcanic activity. Earlier this week, we discussed how solar radiation is among the many problems that face potential human colonization of Mars, but finding a huge underground store of water inside the planet would still go a long way towards making settlement a legitimate possibility. In the long-term, drilling for underground water may be cheaper and easier than, say, trying to melt surface ice, or subsisting off the tiny amount of surface water that we know is present. Additionally, the finding is getting an entire separate crowd excited: those who are hoping to find fossil or other evidence that Mars once supported life. The fact that water has apparently existed on the planet for such a long time makes the odds of life originating there just a little less scant. All this from a pair of meteorites that crashed on our planet over a century ago. Just imagine what we might learn during future missions to Mars, such as NASA’s unmanned space laboratory, Curiosity, which will land on Mars on August 5th. Still, it won’t be easy. Watch this NASA video to learn about the riskiest part of the whole mission—the seven minutes between when the rover hits the top of the Martian atmosphere and when it touches down. By Joseph Stromberg

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A router is a device that directs network traffic destined for an entirely different network in the right direction. For example, suppose your network is having the IP address range of 192.168.1.0/16 and you also have a different network which has a network addresses in range 192.168.2.0/16 . Note that these are ‘Class C’ network addresses which are subnetted. So for your computer ( on the network 192.168.1.0/16 ) to directly communicate between a computer in the network 192.168.2.0/16, you need a intermediary to direct the traffic to the destination network. This is achieved by a router. Configuring Linux as a router Linux can be effectively configured to act as a router between two networks. To activate routing functionality , you enable IP forwarding in Linux. This is how you do this: # echo "1" > /proc/sys/net/ipv4/ip_forward Now you have enabled IP forwarding in Linux. Now make this change persistent across reboots by editing the file /etc/sysctl.conf and entering the following line: #FILE : /etc/sysctl.conf net.ipv4.ip_forward = 1 Optionally, after editing the above file, you may execute the command : # sysctl -p Note: For your linux machine to act as a router, you need two ethernet cards in your machine or you can also configure a single ethernet card to have multiple IP addresses. What is a gateway? Any device which acts as the path to or from your network to another network or the internet is considered to be a gateway. Let me explain this with an example: Suppose your computer, machine_B has an address 192.168.0.5 with default netmask. And another computer (machine_A) with an IP address 192.168.0.1 in your network is connected to the internet using a USB cable modem. Now if you want machine_B to send or recieve data destined for an outside network a.k.a internet, it has to direct it to machine_A first which forwards it to the internet. So machine_A acts as the gateway to the internet. Each machine needs a default gateway to reach machines outside the local network. You can set the gateway in machine_B to point to machine_A as follows: # route add default gw machine_A Or if DNS is not configured… # route add default gw 192.168.0.1 Now you can check if the default gateway is set on machine_B as follows: # route -n What is NAT ? Network Address Translation (NAT) is a capability of linux kernel where the source or destination address / port of the packet is altered while in transit. This is used in situations where multiple machines need to access the internet with only one official IP address available. A common name for this is IP masquerading. With masquerading, your router acts as a OSI layer 3 or layer 4 proxy. In this case, Linux keeps track of the packet(s) journey so that during transmission and recipt of data, the content of the session remains intact. You can easily implement NAT on your gateway machine or router by using Iptables, which I will explain in another post.

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The U.S. officially ended slavery with the passage of the Thirteenth Amendment in 1865. There were various proposals to grant freed black slaves compensation, or at least assistance in establishing themselves as free citizens. Most prominent was General William T. Sherman’s field order granting land to black families near the coasts of South Carolina, Georgia, and Florida, which became known as “forty acres and a mule.” Sherman’s order was rescinded, however, after President Lincoln was assassinated, and the Reconstruction Era left formerly enslaved blacks to fend for themselves. In many cases, former slaves simply remained on plantations as sharecroppers in conditions similar to slavery. In the century following the end of slavery, black Americans faced formidable barriers to political, economic, and social equality. In the South, Jim Crow laws enforced a rigid racial segregation, consigning black citizens to inferior schools and other public services, imposing poll taxes and literacy tests aimed at preventing blacks from voting, and providing official support for a culture of segregation and discrimination. In the North and throughout the rest of the country, there were fewer formal, legal barriers, but rigidly enforced social norms still produced widespread, often blatant segregation and discrimination in employment, housing, schools, churches, and most other aspects of life. Government policies, while not always based formally on race, were frequently designed in ways which benefited whites at the expense of black and other non-white citizens. Race-based violence was also common, and thousands of blacks, and sympathetic whites, were lynched in the South and elsewhere, in waves which occurred periodically from the 1870s until the 1960s. Meanwhile, this century was one of unparalleled social and economic progress for whites, including many whose families arrived as immigrants after the Civil War. The G.I. Bill, the Federal Housing Authority, and other government programs providing substantial aid to provide citizens with access to education, homeownership, jobs and business loans, raising many whites into the middle class. Meanwhile, these programs were often unavailable to blacks, and unofficial policies such as redlining further restricted access to banking, insurance, health care, jobs, and homeownership for black citizens. The net effect of these policies and practices was to widen the racial equality gap in the century leading up to the civil rights movement. In the 1950s and 1960s, there was dramatic progress towards official acceptance of equality for those of all races. The Supreme Court struck down laws segregating schools (Brown v. Board of Education), marriages (Loving v. Virginia) and other public accommodations and institutions Following a series of popular protests lead by Dr. Martin Luther King, Jr. and others, the federal government enacted civil rights legislation designed to end legalized discrimination and to ensure equal access, in practice, to schools, voting booths, housing and jobs. The Civil Rights Era, in changing laws and reshaping public attitudes, and new policies such as affirmative action, began to significantly change circumstances for black Americans. The advances of the 1950s and 1960s, however, were not enough to reverse the failures of Reconstruction or the discrimination of the Jim Crow era. Black Americans made little progress during the century following slavery, while falling further behind white Americans, and progress since that time has been glacially slow by most social and economic indicators. The median net worth of white families has risen to about $121,000, while for black families, the figure is only $19,000. Following the dramatic, government-supported rise in homeownership for whites during the 20th century, it would now take black families, at current rates, about 5,423 years to close the gap in homeownership. Sources: Jonathan Kaplan and Andrew Valls, “Housing Discrimination as a Basis for Black Reparations,” Public Affairs Quarterly (July 2007); Ira Katznelson, When Affirmative Action Was White: An Untold History of Racial Inequality in Twentieth-Century America (New York: W. W. Norton & Co., 2005); Amaad Rivera, Brenda Cotto-Escalera, Anisha Desai, Jeannette Huezo, and Dedrick Muhammad, Foreclosed: State of the Dream 2008 (United for a Fair Economy, 2008).

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In an interview with students, MIT's Kerry Emmanuel stated, "At the end of the day, it's just raw curiosity. I think almost everybody that gets seriously into science is driven by curiosity." Curiosity -- the desire to explain how the world works -- drives the questions we ask and the investigations we conduct. Let's say that we are planning a unit on matter. By having students observe solids and liquids, we have helped them define matter as something that has mass (or weight -- don’t worry about the difference with elementary kids!) and takes up space. The next step is to start thinking about air: "I'm curious, is it matter? Or something else?" The students are now driven by a need to explain if air is or is not matter. The question becomes clear, and we can ask: Is air matter? Next, we can ask our students what data they need to answer the question, and how they can collect that data -- how they can investigate. Students will need to determine if air has mass and/or takes up space. Perhaps they'll suggest that they weigh a basketball multiple times as they use a pump to add more air. Once students conduct the investigation and have data, they can create an explanation. But what does a good explanation look like? According to the CER model, an explanation consists of: - A claim that answers the question - Evidence from students' data - Reasoning that involves a "rule" or scientific principle that describes why the evidence supports the claim Your students might suggest the following explanation: Air is matter (claim). We found that the weight of the ball increases each time we pumped more air into it (evidence). This shows that air has weight, one of the characteristics of matter (reasoning). The explanation could be made more complete by including evidence and reasoning related to air taking up space. Introducing CER to your Students The CER format to writing explanations is not a trivial thing for your students. You will need to explicitly introduce and model it for them. They will need support throughout the year as they get better at writing explanations. The idea that explanations drive science can be illustrated for students by using NASA's aptly named Curiosity Mars Rover. After watching the video about the mission's science goals, ask your students: - What are these scientists curious about -- what do they want to know? - What data will the rover collect? - How will this data help scientists answer -- make claims about -- their questions? Jeff Rohr, a fifth grade teacher in Beaver Dam, Wisconsin, suggests using the following Audi commercial to introduce students to the components of an explanation by asking them to identify the claim, the evidence, and the reasoning – or rule – that connects the evidence to the little girl's claim that her dad is a space alien. Let the Inquiry Begin As you work with your students on CER throughout the year, do the following: - Introduce CER as the "goal" of science - Use concrete (non-science) situations, like mysteries, images, artwork, etc. (Download an example PDF worksheet) - Create an anchor chart - Use a rubric with students to critique examples - Provide examples from science or scientists - Create CER worksheets with data provided by the teacher (Download an example PDF worksheet) - Connect to other content areas (e.g. argumentation in social studies) - Peer Critique

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2003 Virginia SOLs Motivation for Learning Computer Demonstration: Atomic Modeling To give students an idea of the shapes and scales of atoms, link to http://www.colorado.edu/physics/2000/applets/a2.html for a fully interactive periodic table. This table allows teachers and students to explore moving atomic models of each of the first 36 elements. Click on any element's chemical symbol to analyze it. Zoom in on the nucleus to show the closely compacted structure and note how far the electrons orbit from it. The table also provides electron shell configurations and electron potential energies. Remind students of the limitations of the modeling system: electrons follow three-dimensional spherical paths, not simple cirlcular ones as depicted. Also remind them that protons and neutrons are around 2000 times more massive than electrons. Making models of atoms is an activity many teachers use with their students. It emphasizes to the students that atoms are not two-dimensional, fixed entities. Students can make the models in school or at home, and they can use a wide variety of objects-only a few are suggested here. The models constructed have shortcomings in that they are stagnant, and the electrons may appear to be at specified, rather than most probable, distances from the nucleus. Additional Background Information To print out the Student Copy only, click here. Figure 3: Atomic model of an aluminum atom using ¼ in. pom poms as protons (white) and neutrons (black), 1/8 in. pom poms as electrons, and craft wire. Students can explore the interactive online periodic table at http://www.colorado.edu/physics/2000/applets/a2.html. Each student compares the model he/she has created in the student activity with the online version of the atom and notes the successes and deficiencies of each model. Students with Special Needs This may be a difficult activity for students who are unable to manipulate small objects. Rather than working independently, however, students could work with partners or within small groups. Click here for further information on laboratories with students with special needs.

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Isotonic, Hypertonic, and Hypotonic Solutions In this article, we will go over three types of solutions: isotonic, hypertonic and hypotonic solutions. Before we go into the specific types, we will first go over the scenario in which the solution exists. For example, when we talk about the above solutions, these are solutions outside of a substance. For example, say if we place a cell in a solution, which is the example we will use for all the various solutions. The solution outside the cell is what we are referring to when we talk about isotonic, hypertonic, or hypotonic. The solution may be pure water or the solution may be water with a solute dissolved in it, or any such solution. For the below examples, we will use a cell that has a NaCL concentration of 0.9%. So the water concentration inside of it is 99.1%. An isotonic solution is a solution in which the same amount of solute and solution is available inside and outside of the cell. The solution and solute percentage are the same inside the cell as it is in the solution outside in which the cell is placed in. Therefore, using the numbers above, a cell placed in a solution of water with 0.9% NaCL is in equilibrium. Thus, the cell remains the same size. The solution is isotonic in relation to the cell. A hypertonic solution is a solution that contains more solute than the cell which is placed in it. If the cell with a NaCl concentration of 0.9% is placed in a solution of water with a 10% concentration of NaCl, the solution is said to be hypertonic. Hyper means more, meaning the solution that the cell is placed in contains more solute than the solution inside of the cell. When the solution contains more solute, this means that it contains less solution. The solution outside o of the cell is 10% NaCl, which means that it is 90% water. The solution in the cell is 0.9% NaCl, which means it is 99.1%. Remember, solution flows from a higher concentration to a lower concentration. Being that the outside solution is 90% water while the inside contains 99.1% water, water flows from the inside of the cell to the outside solution. Therefore, the cell loses water and shrinks. Even though when we reference a solution to say it is hyper and hypo, we are talking about the amount of solute present in it, when we reference the flow into and out of the cell, we are talking about the solution, not solute. A hypotonic solution is a solution that contains less solute than the cell which is placed in it. If the cell wiht a NaCl concentration is placed in a solution of distilled water, which is pure water with no dissolved substances it, the solution on the outside of the cell is 100% water and 0% NaCl. Inside of the cell, the solution is 99.1% water and 0.9% NaCL. Water, again, goes from a higher concentration to a lower concentration. So water goes from the distilled water solution to the inside of the cell. As a consequence, the cell swells up and possibly bursts. Thus, putting a cell with solute in a distilled water solution will cause swelling and possible bursting of the cell. The main way to remember all of this is that when we talk about the various solutions, we are talking in reference to the outside solution, not the solution inside of the cell. Then, next, when we talk about isotonic, hypertonic and hypotonic solutions, we can use the prefixes and suffixes to determine which is which. The suffix -tonic is in relation to the amount of solute in the solution. Hyper means more, hypo means below. So a hypertonic solution is a solution which contains more solute than the solution inside of the cell. And a hypotonic solution is a solution which contains less solute than the solution inside of the cell. This is the best way to learn this.

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(Picture from the National Archives and Records Administration) World War I was a transformative moment in African-American history. The war directly impacted all African Americans, male and female, northerner and southerner, soldier and civilian. The war years coincided with the Great Migration, one of the largest internal movements of people in American history. Between 1914 and 1920, roughly 500,000 black southerners packed their bags and headed to the North, fundamentally transforming the social, cultural, and political landscape of cities such as Chicago, New York, Cleveland, Pittsburgh, and Detroit. The Great Migrationreshaped black America and the nation as a whole. Black southerners faced many social, economic, and political challenges that made them want to migrate to the North. The majority of black farmers labored as sharecroppers, remained in debt, and lived in poverty. By the time of the war, most black people had been stripped of their right to vote. Jim Crow segregation, legitimized by the Plessy v. Ferguson (1896) Supreme Court ruling, forced black people to use separate and usually inferior facilities. The southern justice system denied them equal protection under the law and condoned the practice of vigilante mob violence. Photographs and Prints Division, Schomburg Center for Research in Black Culture, The New York Public Library. Wartime opportunities in the urban North gave hope to such individuals. The American industrial economy grew significantly during the war (Duffy). Unable to meet demand with existing European immigrants and white women alone, northern businesses increasingly looked to black southerners to fill the void (Sandman). In turn, the prospect of higher wages and improved working conditions prompted thousands of black southerners to abandon their agricultural lives and start anew in major industrial centers (Williams). Black women remained confined to domestic work, while men for the first time in significant numbers made entryways into the northern manufacturing, packinghouse, and automobile industries (Sandman). African-americans did not always get what they expected the north to be (Williams). They frequently endured residential segregation, substandard living conditions, job discrimination, and in many cases, the hostilities of white residents. But life in the North was nevertheless exciting and liberating. No longer subjected to the indignities of Jim Crow and the constant threat of racial violence, southern migrants experienced a new sense of freedom. Most African Americans nevertheless saw the war as an opportunity to demonstrate their patriotism and their place as equal citizens in the nation. "Colored folks should be patriotic," the Richmond Planet insisted. "Do not let us be chargeable with being disloyal to the flag." Black men and women for the most part approached the war with a sense of civic duty. Over one million African Americans responded to their draft calls, and roughly 370,000 black men were inducted into the army (Williams). The military created two combat divisions for African Americans. One, the 92nd Division, was composed of draftees and officers. The second, the 93rd Division, was made up of mostly National Guard units from New York, Chicago, Washington, D.C., Cleveland, and Massachusetts. The two black combat divisions, the 92nd and 93rd, was made up of approximately 40,000 troops. The army assigned the vast majority of soldiers to service units. Black soldiers were stationed and trained throughout the country, although most facilities were located in the South. They had to endure racial segregation and often received substandard clothing, shelter, and social services (Williams). At the same time, the army presented many black servicemen, particularly those from the rural South, with opportunities unavailable to them as civilians, such as remedial education and basic health care. Military service was also a broadening experience that introduced black men to different people and different parts of the country. After The War World War I brought about tremendous change for African Americans and their place in American society. The Great Migration transformed the demographics of black communities in the North and the South. The war effort allowed black men and women to assert their citizenship, hold the government accountable, and protest racial injustice. Military service brought thousands of black men into the army, exposed them to new lands and new people, and allowed them to fight for their country (Williams). Black people staked claim to democracy as a highly personal yet deeply political ideal and demanded that the nation live up to its potential (Sandman). World War I represents a turning point in African American history, one that shaped the course of the black experience in the twentieth century.

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Roller coasters are fast, fun, and exciting! They also involve a lot of Science-potential energy, kinetic energy, velocity, speed, friction, forces, gravity..... Kids can learn about physics by building and testing their own roller coaster. -foam insulating tubes (cut in half to make track) -other recycled materials such as paper towel rolls for tunnels -paper and pencil for planning |Sunshine (age9) adjusting her coaster so that her marble stays on | the track and makes the loop! After designing and testing her rollercoaster, Sunshine wrote two paragraphs explaining how physics is involved in relation to her overall model and coasters in general. She used her Science book, as well as information from websites to guide her with the writing component of this project. Little man had to get in on the action as well! I don't know what's cuter- the red long-johns or his attempt at getting that marble on the coaster? How Roller Coasters Work Hands-on Activity: Amusement Park Ride: Ups and Downs in Design Roller Coaster Marbles: How Much Height to Loop the Loop? Enjoy your weekend!

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The National Science Education Standards mandate that science teachers "plan an inquiry-based program", "focus and support inquiries", and "encourage and model the skills of scientific inquiry." Inquiry is an approach to teaching that involves a process of exploring the natural world, that leads to asking questions and making discoveries in the search of new understandings. Inquiry is a method of approaching problems that is used by professional scientists but is helpful to anyone who scientifically addresses matters encountered in everyday life. Inquiry is based on the formation of hypotheses and theories and on the collection of relevant evidence. There is no set order to the steps involved in inquiry, but children need to use logic to devise their research questions, analyze their data, and make predictions. When using the inquiry methods of investigation, children learn that authorities can be wrong and that any question is reasonable. The most abstract component of inquiry is imagination. Both students and professional scientists have to be able to look at scientific information and data in a creative way. This unconventional vision allows them to see patterns that might not otherwise be obvious. Teachers can incorporate inquiry approaches to learning, for example, by allowing small groups of students to explore a particular natural phenomenon that might exhibit certain trends or patterns. The children can then reconvene as a class, discuss their observations, and compile a list of several different hypotheses from this discussion. Each group can choose a hypothesis to investigate. Several groups might choose to replicate the same study to reduce the bias effects of any one group's techniques. Depending on their age, children might design their own experimental apparatus, use probes attached to computers, or employ sophisticated software to analyze data or create charts and graphs. Data based predictions can be the foundation for further investigation. Inquiry-based learning need not always be a hands-on experience. In fact, doing hands-on science with step-by-step procedures can stifle students' own inquiry, distorts what science is all about, and may impede students' learning. Reading, discussion, and research can allow students to inquire into scientific questions. Teacher can facilitate inquiry in the classroom by: - Acting as facilitators rather than directors of students' learning - Providing a variety of materials and resources to facilitate students' investigations - Modeling inquiry behaviors and skills - Posing thoughtful, open-ended questions and helping students do the same - Encouraging dialogue among students and with the teacher - Keeping children's natural curiosity alive and as a teacher, remaining a curious, life-long learner Many people might say, "Gee, those sound like buzzwords to me. Do they have any substance?" The answer is yes. If children are generating their own ideas in a student-centered classroom, they need the freedom to be physically active in their search for scientific knowledge. How can children begin to understand the nature of the world in which they live if they experience it vicariously? For this reason, the majority of the activities that students perform should be physical explorations. Physical explorations not only make the concepts more tangible but also appeal to children's diverse learning styles and take advantage of their multi-sensory strengths. If children are physically involved, they are more apt to be mentally engaged. Children spontaneously try to explain things that they experience, and feeding their curiosity with the raw materials of potential scientific discoveries promotes this natural theory building. By itself, however, it does not lead to a mature understanding of scientific concepts. The authors of the National Science Education Standards maintain that hands-on activities can increase the probability that students will be engaged in rich inquiry, but do not guarantee that they are learning as intended. Similarly, teaching children abstract concepts without engaging their interest and facilitating their understanding via concrete, experiential examples leads to "shallow" knowledge (or, in many cases, no knowledge at all, as such lessons are quickly forgotten). Scientific concept building is thus a two-way street. Highly abstract concepts are rarely developed spontaneously; such development requires instruction. Nor can in-depth understanding be gained without knowledge of concrete examples to fill out the skeleton of an abstract concept. An inquiry-oriented, "hands on" approach to science instruction stimulates the natural curiosity and theory-building inclination of students while providing a solid conceptual framework for supporting the development of accurate concepts. Such experiences provide the raw material from which mature scientific theories are constructed. To increase a "minds-on" factor to a "hands-on" approach, teachers should decrease the "cookbook" nature of whatever labs they conduct and sequence the hand-s on activities before any readings or lectures so that students can explore topics before learning the terms. (See Learning Cycle for additional information.) JOURNAL ARTICLES - To access most of these Journal Articles, you must be a student, faculty or staff member at an OhioLINK affiliated institution. Access to OhioLINK may be available to Ohioans through their local, public, or school libraries. Contact OPLIN, INFOhio, or your local library for more information. Constructivist Science Teaching: Intellectual and Strategic Teaching Acts Interchange, Vol. 34, Issue: 1, 2003. pp. 63-87 Seatter, Carol Scarff This paper attempts to provide some productive starting points for discussion in the context of science teaching. Embedded in the current practice of methodologies such as "messing about," hands-on, minds-on activities, science-technology-society related approaches, and inquiry-based learning, is often a sense of confusion and frustration. Such current methodologies in elementary science teaching are founded on constructivist learning theory. This paper attempts to pinpoint possible ways in. Teaching the Nature of Inquiry: Further Developments in a High School Genetics Curriculum Science Education, Vol. 9, Issue: 3, May 2000. pp. 247-267 Cartier, Jennifer L.; Stewart, Jim In order for students to truly understand science, we feel that they must be familiar with select subject matter and also understand how that subject matter knowledge was generated and justified through the process of inquiry. Here we describe a high school biology curriculum designed to give students opportunities to learn about genetic inquiry in part by providing them with authentic experiences doing inquiry in the discipline. Since a primary goal of practicing scientists is to construct. An investigation of experienced secondary science teachers' beliefs about inquiry: An examination of competing belief sets Journal of Research in Science Teaching, Vol. 41, Issue: 9, November 2004. pp. 936 - 960 Wallace, Carolyn S.; Kang, Nam-Hwa The purpose of this study was to investigate the beliefs of six experienced high school science teachers about (1) what is successful science learning; (2) what are the purposes of laboratory in science teaching; and (3) how inquiry is implemented in the classroom. An interpretive multiple case study with an ethnographic orientation was used. The teachers' beliefs about successful science learning were substantively linked to their beliefs about laboratory and inquiry implementation. For. Fifth graders' science inquiry abilities: A comparative study of students in hands-on and textbook curricula Journal of Research in Science Teaching, Vol. 43, Issue: 5, May 2006. pp. 467 - 484 Pine, Jerome; Aschbacher, Pamela; Roth, Ellen; Jones, Melanie; McPhee, Cameron; Martin, Catherine; Phelps, Scott; Kyle, Tara et. al. A large number of American elementary school students are now studying science using the hands-on inquiry curricula developed in the 1990s: Insights; Full Option Science System (FOSS); and Science and Technology for Children (STC). A goal of these programs, echoed in the National Science Education Standards, is that children should gain "abilities to do scientific inquiry" and "understanding about scientific inquiry." We have studied the degree to which students can do inquiries by using four. The problem with answers: An exploration of guided scientific inquiry teaching Science Education, Vol. 90, Issue: 3, May 2006. pp. 453 - 467 Furtak, Erin Marie Guided scientific inquiry investigations are designed to have students reach particular answers through the thinking processes and activities of scientists. This presents a difficult challenge for teachers who must selectively hold back answers from students to maintain an atmosphere that encourages student-directed inquiry. The present study explores the different ways that three teachers describe and manage this problem with answers in a middle school physical science investigation. While. Urban African-American middle school science students: Does standards-based teaching make a difference? Journal of Research in Science Teaching, Vol. 37, Issue: 9, November 2000. pp. 1019 - 1041 Kahle, Jane Butler; Meece, Judith; Scantlebury, Kathryn The current reform movement in science education promotes standards-based teaching, including the use of inquiry, problem solving, and open-ended questioning, to improve student achievement. This study examines the influence of standards-based teaching practices on the achievement of urban, African-American, middle school science students. Science classes of teachers who had participated in the professional development (n = 8) of Ohio's statewide systemic initiative (SSI) were matched with. Inquiry-based instruction in secondary agricultural education: problem solving revisited. Contains many references that discuss the various aspects of inquiry-based instruction; a good summary of the major concepts.

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Get to know the geometry of the line with this worksheet, which also goes over parallel and perpendicular lines. On this worksheet, your third-grader will be asked to find the right angles and label them with the right angle symbol. On this worksheet, your third-grader will be asked to circle all the right angles he can find in the picture. On this geometry worksheet, your third-grader will look at the different triangles and label them as equilateral, isosceles or scalene Searching for a worksheet to help you child with spatial awareness? This printable shape quiz works with basic geometric shapes. Help your third-grader learn to recognize the identifying features of a polygon on this geometry worksheet. Help your third-grader learn to recognize quadrilaterals with this geometry worksheet. Learn some basic geometry with this worksheet all about the angle. Give your child some practice identifying lines, line segments, and rays with this geometry worksheet.

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For many students with disabilities—and for many without—the key to success in the classroom lies in having appropriate adaptations, accommodations, and modifications made to the instruction and other classroom activities. Some adaptations are as simple as moving a distractible student to the front of the class or away from the pencil sharpener or the window. Other modifications may involve changing the way that material is presented or the way that students respond to show their learning. Adaptations, accommodations, and modifications need to be individualized for students, based upon their needs and their personal learning styles and interests. It is not always obvious what adaptations, accommodations, or modifications would be beneficial for a particular student, or how changes to the curriculum, its presentation, the classroom setting, or student evaluation might be made. This page is intended to help teachers and others find information that can guide them in making appropriate changes in the classroom based on what their students need. Part 1: A Quick Look at Terminology You might wonder if the terms supports, modifications, and adaptations all mean the same thing. The simple answer is: No, not completely, but yes, for the most part. (Don’t you love a clear answer?) People tend to use the terms interchangeably, to be sure, and we will do so here, for ease of reading, but distinctions can be made between the terms. Sometimes people get confused about what it means to have a modification and what it means to have an accommodation. Usually a modification means a change in what is being taught to or expected from the student. Making an assignment easier so the student is not doing the same level of work as other students is an example of a modification. An accommodation is a change that helps a student overcome or work around the disability. Allowing a student who has trouble writing to give his answers orally is an example of an accommodation. This student is still expected to know the same material and answer the same questions as fully as the other students, but he doesn’t have to write his answers to show that he knows the information. What is most important to know about modifications and accommodations is that both are meant to help a child to learn. Back to top Part 2: Different Types of Supports By definition, special education is “specially designed instruction” (§300.39). And IDEA defines that term as follows: (3) Specially designed instruction means adapting, as appropriate to the needs of an eligible child under this part, the content, methodology, or delivery of instruction—(i) To address the unique needs of the child that result from the child’s disability; and(ii) To ensure access of the child to the general curriculum, so that the child can meet the educational standards within the jurisdiction of the public agency that apply to all children. [§300.39(b)(3)] Thus, special education involves adapting the “content, methodology, or delivery of instruction.” In fact, the special education field can take pride in the knowledge base and expertise it’s developed in the past 30-plus years of individualizing instruction to meet the needs of students with disabilities. It’s a pleasure to share some of that knowledge with you now. Sometimes a student may need to have changes made in class work or routines because of his or her disability. Modifications can be made to: - what a child is taught, and/or - how a child works at school. Jack is an 8th grade student who has learning disabilities in reading and writing. He is in a regular 8th grade class that is team-taught by a general education teacher and a special education teacher. Modifications and accommodations provided for Jack’s daily school routine (and when he takes state or district-wide tests) include the following: - Jack will have shorter reading and writing assignments. - Jack’s textbooks will be based upon the 8th grade curriculum but at his independent reading level (4th grade). - Jack will have test questions read/explained to him, when he asks. - Jack will give his answers to essay-type questions by speaking, rather than writing them down. Modifications or accommodations are most often made in the following areas: Scheduling. For example, - giving the student extra time to complete assignments or tests - breaking up testing over several days Setting. For example, - working in a small group - working one-on-one with the teacher Materials. For example, - providing audiotaped lectures or books - giving copies of teacher’s lecture notes - using large print books, Braille, or books on CD (digital text) Instruction. For example, - reducing the difficulty of assignments - reducing the reading level - using a student/peer tutor Student Response. For example, - allowing answers to be given orally or dictated - using a word processor for written work - using sign language, a communication device, Braille, or native language if it is not English. Because adapting the content, methodology, and/or delivery of instruction is an essential element in special education and an extremely valuable support for students, it’s equally essential to know as much as possible about how instruction can be adapted to address the needs of an individual student with a disability. The special education teacher who serves on the IEP team can contribute his or her expertise in this area, which is the essence of special education. One look at IDEA’s definition of related services at §300.34 and it’s clear that these services are supportive in nature, although not in the same way that adapting the curriculum is. Related services support children’s special education and are provided when necessary to help students benefit from special education. Thus, related services must be included in the treasure chest of accommodations and supports we’re exploring. That definition begins: §300.34 Related services. (a) General. Related services means transportation and such developmental, corrective, and other supportive services as are required to assist a child with a disability to benefit from special education, and includes… Here’s the list of related services in the law. - speech-language pathology and audiology services - interpreting services - psychological services - physical and occupational therapy - recreation, including therapeutic recreation - early identification and assessment of disabilities in children - counseling services, including rehabilitation counseling - orientation and mobility services - medical services for diagnostic or evaluation purposes - school health services and school nurse services - social work services in schools This is not an exhaustive list of possible related services. There are others (not named here or in the law) that states and schools routinely make available under the umbrella of related services. The IEP team decides which related services a child needs and specificies them in the child’s IEP. Read all about it in our Related Services page. Supplementary Aids and Services One of the most powerful types of supports available to children with disabilities are the other kinds of supports or services (other than special education and related services) that a child needs to be educated with nondisabled children to the maximum extent appropriate. Some examples of these additional services and supports, called supplementary aids and services in IDEA, are: - adapted equipment—such as a special seat or a cut-out cup for drinking; - assistive technology—such as a word processor, special software, or a communication system; - training for staff, student, and/or parents; - peer tutors; - a one-on-one aide; - adapted materials—such as books on tape, large print, or highlighted notes; and - collaboration/consultation among staff, parents, and/or other professionals. The IEP team, which includes the parents, is the group that decides which supplementary aids and services a child needs to support his or her access to and participation in the school environment. The IEP team must really work together to make sure that a child gets the supplementary aids and services that he or she needs to be successful. Team members talk about the child’s needs, the curriculum, and school routine, and openly explore all options to make sure the right supports for the specific child are included. Much more can be said about these important supports and services. Visit our special article on Supplementary Aids and Services to find out more. Program Modifications or Supports for School Staff If the IEP team decides that a child needs a particular modification or accommodation, this information must be included in the IEP. Supports are also available for those who work with the child, to help them help that child be successful. Supports for school staff must also be written into the IEP. Some of these supports might include: - attending a conference or training related to the child’s needs, - getting help from another staff member or administrative person, - having an aide in the classroom, or - getting special equipment or teaching materials. The issue of modifications and supports for school staff, so that they can then support the child across the range of school settings and tasks, is also addressed in our article on Program Modifications for School Personnel. Accommodations in Large Assessments IDEA requires that students with disabilities take part in state or district-wide assessments. These are tests that are periodically given to all students to measure achievement. It is one way that schools determine how well and how much students are learning. IDEA now states that students with disabilities should have as much involvement in the general curriculum as possible. This means that, if a child is receiving instruction in the general curriculum, he or she could take the same standardized test that the school district or state gives to nondisabled children. Accordingly, a child’s IEP must include all modifications or accommodations that the child needs so that he or she can participate in state or district-wide assessments. The IEP team can decide that a particular test is not appropriate for a child. In this case, the IEP must include: - an explanation of why that test is not suitable for the child, and - how the child will be assessed instead (often called alternate assessment). Ask your state and/or local school district for a copy of their guidelines on the types of accommodations, modifications, and alternate assessments available to students. Even a child with many needs is to be involved with nondisabled peers to the maximum extent appropriate. Just because a child has severe disabilities or needs modifications to the general curriculum does not mean that he or she may be removed from the general education class. If a child is removed from the general education class for any part of the school day, the IEP team must include in the IEP an explanation for the child’s nonparticipation. Because accommodations can be so vital to helping children with disabilities access the general curriculum, participate in school (including extracurricular and nonacademic activities), and be educated alongside their peers without disabilities, IDEA reinforces their use again and again, in its requirements, in its definitions, and in its principles. The wealth of experience that the special education field has gained over the years since IDEA was first passed by Congress is the very resource you’ll want to tap for more information on what accommodations are appropriate for students, given their disability, and how to make those adaptations to support their learning.

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The Mean and Median: Measures of Central Tendency The mean and the median are summary measures used to describe the most "typical" value in a set of Statisticians refer to the mean and median as measures of central The Mean and the Median The difference between the mean and median can be illustrated with an example. Suppose we draw a sample of five women and measure their weights. They weigh 100 pounds, 100 pounds, 130 pounds, 140 pounds, and 150 When statisticians talk about the mean of a they use the Greek letter μ to refer to the mean score. When they talk about the mean of a statisticians use the symbol x to refer to the mean score. The Mean vs. the Median As measures of central tendency, the mean and the median each have advantages and disadvantages. Some pros and cons of each measure are summarized below. - The median may be a better indicator of the most typical value if a set of scores has an outlier. An outlier is an extreme value that differs greatly from other values. - However, when the sample size is large and does not include outliers, the mean score usually provides a better measure of central tendency. To illustrate these points, consider the following example. Suppose we examine a sample of 10 households to estimate the typical family income. Nine of the households have incomes between $20,000 and $100,000; but the tenth household has an annual income of $1,000,000,000. That tenth household is an outlier. If we choose a measure to estimate the income of a typical household, the mean will greatly over-estimate the income of a typical family (because of the outlier); while the median will not. Effect of Changing Units Sometimes, researchers change units (minutes to hours, feet to meters, etc.). Here is how measures of central tendency are affected when we change units. - If you add a constant to every value, the mean and median increase by the same constant. For example, suppose you have a set of scores with a mean equal to 5 and a median equal to 6. If you add 10 to every score, the new mean will be 5 + 10 = 15; and the new median will be 6 + 10 = 16. - Suppose you multiply every value by a constant. Then, the mean and the median will also be multiplied by that constant. For example, assume that a set of scores has a mean of 5 and a median of 6. If you multiply each of these scores by 10, the new mean will be 5 * 10 = 50; and the new median will be 6 * 10 = 60. Test Your Understanding Four friends take an IQ test. Their scores are 96, 100, 106, 114. Which of the following statements is true? I. The mean is 103. II. The mean is 104. III. The median is 100. IV. The median is 106. (A) I only (B) II only (C) III only (D) IV only (E) None is true The correct answer is (B). The mean score is computed from the equation: Mean score = Σx / n = (96 + 100 + 106 + 114) / 4 = 104 Since there are an even number of scores (4 scores), the median is the average of the two middle scores. Thus, the median is (100 + 106) / 2 = 103.

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On this day in 1783, Virginia cedes the vast territory it had previously claimed by right of colonial charter to the federal government of the United States. The Ohio Valley territory, which covered the area north of the Ohio River, east of the Mississippi River, and south of the Great Lakes and Canada, had been contested by Pennsylvania, New York, Massachusetts and Connecticut. A young George Washington began the Seven Years’ War with a failed attempt to secure Virginia’s Ohio Valley outposts in 1754. For some, the British Proclamation line of 1763, banning further European settlement west of Appalachia had been a major incentive for rebellion. To complicate matters, Congress and the states had promised their soldiers land in payment for their service during the War for Independence. The states without western claims worried that they would forever be poor relations without western land to sell and fill their coffers. The new and fragile union remained at risk of dissolution until the land-claims issue found resolution. Pennsylvanian John Dickinson first suggested that the states cede their lands to the Continental Congress in 1776. Virginia argued that their western claims superceded those of any of the other states because they were made in the first colonial charter, but the desire of leading Virginians for a stable confederated government outstripped their desire for land. They were the first state to cede significant holdings to the national government. Other states soon followed suit, solidifying the strength and wealth of the union and making western expansion a federal project, which culminated in Jefferson’s brilliantly conceived Northwest Ordinance.

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TEACHERS SHOULD PREVIEW ALL CONTENT PRIOR TO SHARING WITH STUDENTS. Suggested Grade Level: 5-8 This research guide serves as a resource for the Rock and Roll Hall of Fame and Museum's Education Department course, Rock and Roll & the Science of Sound. For additional information on the course and for more teacher resources, see http://www.rockhall.com/education/inside-the-classroom/rockin/SOS/ We typically think of music as an art form, but every note we hear can be understood in relation to the laws of science. This class examines the basic acoustic principles in the sounds of rock and roll by investigating how all sounds are created by vibrations, how sound travels to our ears through moving air molecules, and how sounds can be represented in a graph by using an oscilloscope or a computer. Students will learn how the musical notes of instruments are determined by frequency and amplitude and how the shape of a waveform determines an instrument’s timbre. Musical examples showcase Rock and Roll Hall of Fame Inductees and illustrate how we perceive the various elements of sound. The class concludes with a live demonstration of digital audio software in which audience volunteers get to record and manipulate their own voices. Our catalog has a subject category for "Inductee." If you enter this term in the search box and choose "Subject" in the dropdown box, you will retrieve information on our resources that are related to Rock and Roll Hall of Fame Inductees. Limit your search by using the facets on the left of your screen in the library catalog, i.e. Format: These research databases can be accessed within the Library and Archives. These resources, pulled from class discussion and selected from the Library and Archives' collections, will help you to: Rock and Roll Hall of Fame and Museum | Library and Archives 2809 Woodland Avenue | Cleveland, OH 44115 | 216.515.1956 | firstname.lastname@example.org

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This activity investigates how you might make squares and pentominoes from Polydron. If you had 36 cubes, what different cuboids could you make? How can you put five cereal packets together to make different shapes if you must put them face-to-face? Semaphore is a way to signal the alphabet using two flags, one held in each hand. To send a message, your left and right hands have to be in two different positions. You start with both hands pointing down. Here are the signals for the letters of the alphabet: Image by kind permission of http://inter.scoutnet.org/ What does this message say? You might want to send a message that contains more than just letters (exclamation marks, question marks, full stops etc). How many other symbols could you send using this code? This offers an interesting exploration of systematically finding combinations. Children may need to discuss whether there is a difference between the right hand being at 12 o'clock, compared with the left hand.

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Voltage: Ohm's Law and Kirchhoff's Rules Ohm's Law and Kirchhoff's rules is fundamental for the understanding of dc circuit. This experiment proves and show how these rules can be applied to so simple dc circuits. In the theory of Ohm's Law, voltage is simply proportional to current as illustrated in the proportionality, V=RI. As shown in this relation, V represent voltage which is the potential difference across the two ends of a electrical conductor and between which an electric current , I, will flow. The constant, R, is called the conductor's resistance. Thus by the Ohm's Law, one can determine the resistance R in a DC circuit without measuring it directly provided that the remaining variable V and I is known. A resistor is a piece of electric conductor which obeys Ohm's Law and has been designed to have a specific value for its resistance. As an extension of the Ohm's Law, two more relationship can be drawn for electric circuits containing resistors connected in series or/and parallel. For resistors connected in series, the sum of their resistance is, RTOTAL=R1+R2+ ..... +Rn . And for resistors connected in parallel, 1/RTOTAL==1/R1+1/R2+ ..... +1/Rn . Complex dc circuit involving a combination of parallel and series resistors can be analyzed to find the current and voltage at each point of the circuit using 2 formulated by Kirchhoff. 1) The algebraic sum of current at any branch point in a circuit is zero. 2) The algebraic sum of potential difference, V, around any closed loop in a circuit is zero. These rules and equations provided by the Ohm's law and the Kirchhoff rule can be experimentally tested with the apparatus available in the lab The apparatus used in the experiment includes a Voltmeter, an Ammeter, some connecting wires and a series of resistors and light bulb with varies resistance. This experiment could be divided into 5 sections which value of voltage and current measured is noted in all sections for further calculation. In the first section, in order to evaluate the reliability of Ohm's law, a dc circuit was constructed as FIG 2 (on p.4 ) using a resistor with an expected resistance at 2400W*120W. In the second section, we were instructed to determine the internal resistance of the voltmeter. Two dc circuit were constructed as FIG 1. and FIG 2. using a resistor with an expected resistance at 820000W*41000W. In the third section, we were asked to judge if the filament of a light bulb obey Ohm's law, this was done by constructing a dc circuit as FIG 1. with a light bulb instead of a resistor. Where in the forth section of the experiment, we explored the ability of multimeter to measure resistance directly and observed the difference in total resistance when two resistor at 270W*14W and 690W*35W were connected parallel or series together. And finally, in the last section of this experiment, we were instructed to construct a circuit like the one shown in FIG 3. and test the Kirchhoff's rules where R1, R2, R3 are 270W*14W, 690W*35W and 2400W*120W respectively. The voltage and current across and through each resistor was measured. RESULTS AND DISCUSSION Results from section 1 as we saw on Graph 1, the calculated resistance was constant at 2448W*147W and this was within the experimental error of the actual resistance of the resistor and so proved the accuracy of Ohm's law. Graph 2 and 3 summarized the differences in total resistance led to the finding of the voltmeter's internal resistance in section 2. Since the calculated total resistance , R1total , from circuit constructed as FIG 1. was, Resistor ,the resistance of the resistor alone, on the other hand, the calculated total resistance, R2total , from circuit constructed as FIG 2. was , 1/Rresistor+1/ Internal resistance , a combination of resistance of resistor and internal resistance of the voltmeter. Though a series of mathematical calculation, Internal resistance can be solved. Our calculated Internal resistance is 18.21MW*0.02MW which was much greater than the expected value of 10MW. This error is most likely due to 1) the inaccurate value of given internal resistance since it's unlikely that all voltmeter have the same internal resistance. 2) Unstability of power supply causes reading error. Graph 4 shown that growing light bulb did not obey Ohm's law. Its resistance increased as it became brighter. The fact that resistance of a metal increases with temperature is largely due to the heat, or kinetic vibration built up in metal interferes with flow of electrons. In the fourth section of the experiment, the resistance measured in parallel and series is 191W*1W and 950W*5W, very similar to the calculated resistance which is 194W*13W and 960W*37W respectively. And in our last section, to verify Kirchhoff's rules, I2+I3=3.70mA*0.04mA is approximately equal to I1 which is 3.79mA*0.03mA. Also, Vbattery+V1+V2= Battery +V1+V3 where both are equal to 0V. This experiment show that most dc circuit problems can be solve by Ohm's law and Kirchhoff's rules which interested in voltage current and resistance. M.M.Sternheim, J.W.Kane. General Physics 2nd edition John Wiley & Sons, Inc. 1991. Canada. p.434-435 F.Hynds. First Year Physics Laboratory Manual 1995-1996 University of Toronto Bookstores. 1995. Toronto, Canada. p.74-76

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Loyalists were American colonists, of different ethnic backgrounds, who supported the British cause during the American Revolution (1775–83). Loyalists were American colonists, of different ethnic backgrounds, who supported the British cause during the American Revolution (1775–83). Tens of thousands migrated to British North America during and after the revolutionary war — boosting the population and heavily influencing the politics and culture of what would become Canada. As American rebels fought for independence from Britain, Loyalists supported the "mother country" for different reasons. Many felt a personal loyalty to the Crown, or were afraid that revolution would bring chaos to America. Many agreed with the rebels’ view that America had suffered wrongs at the hands of Britain, but believed the solution could be worked out within the British Empire. Others saw themselves as weak or threatened within American society and in need of an outside defender. These included linguistic and religious minorities, recent immigrants not fully integrated into American society, as well as Black and Aboriginal people. Others were simply attracted by free land and provisions. Sympathy for the Crown was a dangerous sentiment; those who defied the revolutionary forces could find themselves without civil rights, subject to mob violence, or flung into prison. Loyalist property was vandalized and often confiscated. During the Revolution more than 19,000 Loyalists served Britain in specially created provincial militia corps, accompanied by several thousand Aboriginal allies. Others spent the war in such strongholds as New York City and Boston, or in refugee camps such as those at Sorel and Machiche, Québec. Between 80,000 and 100,000 eventually fled, about half of them to Canada. Who Were They? The vast majority of Loyalists were neither well-to-do nor particularly high in social rank; most were farmers, labourers, tradespeople and their families. They were of varied cultural backgrounds, and many were recent immigrants. White Loyalists brought large numbers of slaves with them. Until 1834, slavery was legal in all British North American colonies but Upper Canada, where the institution was being phased out. Free Blacks and escaped slaves who had fought in the Loyalist corps, as well as about 2,000 Aboriginal allies — mainly Six Nations Iroquois from New York State — also settled in Canada. In 1789, Lord Dorchester (see Guy Carleton), governor-in-chief of British North America, proclaimed that the Loyalists and their children should be allowed to add "UE" to their names, "alluding to their great principle, the Unity of Empire." As a result, the phrase "United Empire Loyalist," or UEL, was applied to Loyalists who migrated to Upper and Lower Canada. (The term was not officially recognized in the Maritimes until the 20th century.) In determining who among its subjects was eligible for compensation for war losses, Britain used a fairly precise definition: Loyalists were those born or living in the American colonies at the outbreak of the Revolution who rendered substantial service to the royal cause during the war, and who left the United States by the end of the war or soon after. Those who left substantially later — mainly to gain land and to escape growing racial intolerance — are often called "late" Loyalists. The main waves of Loyalists came to what is now Canada in 1783 and 1784. The territory that became the Maritime provinces became home to more than 30,000. Most of coastal Nova Scotia received Loyalist settlers, as did Cape Breton and Prince Edward Island (then called St. John’s Island). The two principal settlements were in the Saint John River valley in what is now New Brunswick, and temporarily at Shelburne, Nova Scotia. The Loyalists swamped the existing population in the Maritimes, and in 1784 the colonies of New Brunswick and Cape Breton were created to deal with the influx. Of about 2,000 who moved to present-day Québec, some settled in the Gaspé, on Chaleur Bay, and others in Sorel, at the mouth of the Richelieu River. About 7,500 moved into what would become Ontario, most settling along the St. Lawrence River to the Bay of Quinte. There were also substantial settlements in the Niagara Peninsula and on the Detroit River, with subsidiary and later settlements along the Thames River and at Long Point. The Grand River was the main focus of Loyalist Iroquois settlement. The Loyalist influx gave the region its first substantial population and led to the creation of a separate province, Upper Canada, in 1791. Loyalists were instrumental in establishing educational, religious, social and governmental institutions. Though greatly outnumbered by later immigrants, Loyalists and their descendants, such as Egerton Ryerson, exerted a strong and lasting influence. Modern Canada has inherited much from the Loyalists, including a certain conservatism, a preference for "evolution" rather than "revolution" in matters of government, and tendencies towards a pluralistic and multi-ethnic society. E.C. Wright, The Loyalists of New Brunswick (1955) W. Brown, The Good Americans (1969) M.B. Fryer, King's Men (1980) B. Graymont, The Iroquois in the American Revolution (1972) Bruce G. Wilson, As She Began (1981)

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In Honor of Black History Month, we wanted to recognize and commemorate a few events and persons that have created a lasting impression on our history. Today we spotlight Rosa Parks, a courageous woman who helped pave the path to end segregation of public facilities. On December 1, 1955 in Montgomery, Alabama, Rosa Parks refused to give up her seat to a White passenger. In doing so, she defied the law that African American passengers give up their seats located in the back of the bus to White passengers if no other seats are available. She was arrested and fined for standing her ground. Her bold act began The Montgomery Bus Boycott. This was a 381 day boycott of Montgomery busses that resulted in the ability for blacks and whites to ride the buses as equals. Rosa Parks was, and still is an inspiration to many, showing that one person can make an impact. Share Rosa Parks’ story with your class with one of Discovery Educations videos. Check out “Standing Up for Freedom: The Story of Rosa Parks” for a good overview of her achievement. Engage your students this month with various resources dedicated to Black History Month. How are you commemorating Black History Month in your classroom?

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Difference Between Density and Volume Density vs Volume Density and volume are two scientific concepts that pertain to the physical properties and characteristics of matter. These properties often describe the quality or property of a given object. Both concepts are usually encountered in the field of physics and both act as measurement tools for three-dimensional objects. But both properties can be applied for three stages or states of matter which are; solid, liquid, and gas. “Density” is defined as the mass per unit of volume. To put it simply, it tackles the concept of how much matter or mass is inside an object in the space that it occupies. It also describes the relationship between an object’s mass and volume. Density is symbolized by the letter “D” and is a scalar quantity of matter. The formula is p = M/V, or density equals the mass divided by the volume. This formula is only applicable for objects with uniform compositions or solid objects. By this same formula, with a few adjustments, the formula for volume and mass can also be derived. In experiments, mass is often determined first before the volume. Density is measured in the following units: pounds per cubic foot, grams per cubic centimeter, and kilograms per cubic centimeter. Different substances have different densities. Due to this fact, this property of matter can be used to determine if a certain sample or substance is genuine or not. Density can change or vary when temperature or pressure is applied. Volume, in comparison, is a component of density. As a property, volume is concerned with how much space a particular object occupies. It is represented by the letter “V.” In finding density, volume is one of the two key components; the other one being mass. In a three-dimensional object, the shape’s volume can be determined by multiplying the dimensions, which comprise of the object’s length, width, and height. Specific shapes like a cube, cylinder, prism, rectangular prism, pyramid, cone, circle, sphere and other shapes have specific formulas in determining volume. For liquids and gases, the sample substances are put into a container and calculated. Volume is expressed in units and subunits like cubic meters for solids and cubic liters for liquids and gases. Density and volume have an inverse relationship with each other. If density increases, the effect will be the decrease of volume. In contrast, if the volume increases, density decreases. 1.Both density and volume are physical properties of matter. They are present in the traditional stages of matter which are solid, liquid, and gas. Both density and volume have a specific formula regarding solids or regular-shaped objects. In measuring liquids and gases, there is a little deviation from the traditional approach or formula. 2.Density is represented by the letter “D” while volume is recognized using the letter “V.” 3.Density measures the amount of matter present in the object. Meanwhile, volume is concerned about the amount of space that an object occupies. 4.The density formula for solid or three-dimensional objects comprises two components, mass and volume. In this view, volume is a component of density. On the other hand, the volume of a regular shape is determined by three dimensions: length, width, and height. In many instances, volume is measured by the use of a graduated cylinder, water, and a specific object. 5.In terms of units, density units are a composite and involve the mass and volume components. In contrast, there is only one component involved in the volume, which is the unit used for volume only. 6.Density and volume have inverse relationships in accordance to the mathematical formula for density. 7.Density and volume are very important concepts to consider especially in experiments. Determining these properties are very helpful in combining or working with substances. Search DifferenceBetween.net : Email This Post : If you like this article or our site. Please spread the word. Share it with your friends/family. Leave a Response

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Children "analyze and compare two- and three-dimensional shapes" and describe similarities, differences and attributes (K.G.4). Attributes are the same things as properties--they are things that we describe as being the same or different between shapes. In first grade, children should "distinguish between defining attributes ... versus non-defining attributes... [and] build and draw shapes to possess defining attributes." (1.G.1) Lesson 1 discussed defining attributes of the standard shapes (triangle, square, rectangle), this lesson looks at geometric attributes that are shared by some triangles or quadrilaterals. This ties into "recogniz[ing] and draw[ing] shapes having specified attributes" (2.G.1) and "understand[ing] that shapes in different categories ... may share attributes... , and that the shared attributes can define a larger category" (3.G.1). Sorting triangles by angle measurements Angles are categorized as right (if their measurement is 90°--half of a straight angle), acute (if it is less than a right angle) or obtuse (if it is greater than a right angle. One way of translating that into classifying about triangles is to say that it is obtuse if its largest angle is obtuse, right if its largest angle is right, and acute if its largest angle is acute. Sometimes that seems a little confusing with, for example, an equilateral triangle where all of the angles are the same size, so another way to describe acute triangles is that they have all 3 angles acute. These categories fit nicely--the triangles look like they go together. Children likely to first describe the triangles using informal language (tall and narrow/short and wide). The more formal language that we use to describe the triangles by their angles is important, however, for understanding shapes because it turns a description that makes most sense if the triangles are in one orientation (with a particular side horizontally on the bottom) to a description that makes sense for the triangles no matter how you turn them. You can, for instance, turn a tall narrow triangle into a short, wide triangle by turning it on its side, but when we come up with attributes to describe geometric shapes, we want to use attributes and descriptions that don't change when we turn the triangle. Sorting triangles by side lengths Triangles are called equilateral if all of the sides have the same length. Triangles are called isosceles if two sides are the same length. Sometimes in math class we say that triangles are isosceles if they have two and only two sides the same length, and sometimes we say that they are isosceles if they have at least two triangles the same length. Probably it's safer to say that triangles are isosceles if they have at least two sides the same length--that means equilateral triangles are a special kind of isosceles triangle, just like squares are a special kind of rectangle. Triangles are called scalene if all of the sides are different lengths. Each triangle can be sorted both by their side lengths and by their angle measures Isosceles triangles can be acute, right or obtuse Scalene triangles can be acute, right or obtuse Equilateral triangles are always acute, they are never right or obtuse. You can make all of the kinds of isosceles and scalene triangles on a geoboard, but you can never make an equilateral triangle on a geoboard (you can get really close, but not quite). An extra note about geoboards: When you're looking at measurements on a geoboard there are a couple of mistakes it's easy to make. The first is that when you are measuring lengths, you could be counting dots instead of lengths in between. The length should be the number of spaces (think of each space as an inch), not the number of dots. The other thing to watch out for is that you can't just count diagonally to find diagonal lengths. The distance between two diagonally adjacent pegs is greater than the vertical or horizontal distance between two adjacent pegs. (It's not a simple fraction to tell how much longer, either--you need the Pythagorean theorem for that!) Polygons that have 4 sides are quadrilaterals. There are even more named varieties of quadrilaterals than there are varieties of triangles. All of the shapes in this image are quadrilaterals One property that quadrilaterals can have is that they can have parallel opposite sides. If each side has a parallel opposite side (two pairs of parallel sides), the shape can be called a parallelogram. Everything in the green loop is a parallelogram. Rectangles, squares and rhombuses (rhombi) are parallelograms because their opposite sides are always parallel. It's also correct to say that a quadrilateral is a parallelogram if its opposite sides are the same length, but usually in the definition we use that the opposite sides are parallel because the word parallel is part of parallelogram. A rhombus has all 4 sides equal length. O is a rhombus, and it's sneaky, but the square P is a rhombus too. (Squares get to be a lot of different things besides just squares). Quadrilaterals that have one pair of parallel sides are called trapezoids. M, N and U are all trapezoids. Some math books (and lots of mathematicians) say that a trapezoid has at least on pair of parallel sides, so that would make a parallelogram (with two pairs of parallel sides like K, O, P and Q) just a special kind of a trapezoid. Other math books (includingmost of the high school geometry books I've looked at recently) say that trapezoids have one and only one pair of parallel sides. Because words get their meaning from what groups of people agree that they mean, there isn't a right or a wrong definition of trapezoid. Sometimes we give special names to other shapes too. R, for instance, is a kite because it has two pairs of sides that are adjacent (next to each other) that are the same length. Like "trapezoid", there isn't just one definition of "kite"--some people would say that L is also a kite because it has two pairs of adjacent sides that are the same length, and other people would say it is not a kite because it's concave. Every triangle can be classified by its angles and by its side lengths, but there are some quadrilaterals that don't have any special classification at all. H and I, for example, aren't part of any named group of quadrilaterals. One important idea about classifying shapes is that the same shape can fit into more than one category, and some categories are subsets of other categories. For example: |A square is a special kind of rectangle. All squares are rectangles. Some rectangles are squares, and some rectangles are not squares.| |A square is also a special kind of a rhombus. All squares are rhombi (or rhombuses). Some rhombi are squares, and some are not squares.| |A square is a rectangle and also a rhombus. Everything that is both a rectangle (90° angles) and a rhombus (all equal sides) is a square.| |Squares, rectangles and rhombi all have parallel sides, so they are all parallelograms. There are some parallelograms that don't fit rectangles, rhombi or squares.| All of these shapes (as well as trapezoids, kites, and a few others) are quadrilaterals because they all have 4 sides.

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Copyright © University of Cambridge. All rights reserved. Students grow accustomed to thinking that calculating an average gives you all the information you need to know about a set of data. In this problem, the data are chosen in such a way that calculating averages is not enough to distinguish between the sets, but looking at the shape of the distributions makes the differences clear. In order to compare the distributions, students could use statistical techniques such as stem-and-leaf diagrams, box-and-whisker diagrams, and bar charts or histograms. Introduce the problem. "The numbers in the six lists all seem to be quite similar. What statistical techniques could we use to try to spot differences between the data sets?" Give students some time to discuss in pairs the sort of techniques they might use, and then collect together ideas on the board. "Your challenge is to work out which data sets belong to Alison and which ones belong to Charlie. You need to be pretty sure of your answer and have some supporting evidence to convince others that you are right." If a computer room is available, students may work in pairs and use the statistical tools in a spreadsheet program to prepare graphs or diagrams. (GeoGebra, which is free to download and use, includes a spreadsheet tool and can be used to draw box-and-whisker diagrams and histograms.) If a computer room is not available, encourage students to work in small groups so that they can decide together what sort of calculations and diagrams to use, and then share out the drawing of the diagrams before coming together again to compare the results. As the class are working, note any good practice and stop the class when appropriate to share it. Finally, allow plenty of time for groups to report back. In their reports to the class, they should include their answer to the problem and the statistical evidence that convinced them of their answer. At the end, there could also be some general discussion about the merits of different techniques that were tried (with reference to methods that didn't work as well as those that did.) Which statistical techniques might be useful for comparing the data sets? What are the key features of the diagrams you can draw to represent the data sets? Take a look at Data Matching for a more challenging problem that requires students to use similar statistical techniques with more complex distributions. Suggest students set out the data using stem-and-leaf diagrams (and/or bar charts) and box-and-whisker diagrams. Then ask them to describe the key features of each distribution, and identify which key features the different sets have in common.

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Methane in the Earth's atmosphere is an important greenhouse gas, so far accounting for about 20 percent of the global warming caused by human activity — more than any other gas except CO2. It has a global warming potential of 34 over a 100-year period, and 86 over a 20-year period, meaning that a methane emission will have 34 times the impact on temperature of a CO2. emission of the same mass over the next 100 years and 86 times the impact over a 20-year period. Methane has a big impact over a brief period — a lifetime of about 12 years in the atmosphere — whereas CO2. has a smaller impact for a far longer period of more than 100 years. An estimated 60 percent of the Earth’s methane emissions are attributable to human activity, with landfills, livestock husbandry, fossil fuel development, and rice agriculture as major causes. Methane is also naturally released by the decay of organic matter in wetlands. Less significant natural sources include termites, oceans, and release from methane deposits buried deep within the Earth. Currently, the amount of methane released by those deposits is slight in comparison to other sources — but shifts in the planet’s stability, of the magnitude expected from continued rapid global warming, could cause massive releases of stored methane. In particular, Arctic methane could prove to be the linchpin for runaway global warming. Thousands of years ago, billions of tons of methane were created by decaying Arctic plants, which now lies frozen in permafrost and trapped in the ocean floor. As the Arctic warms, this methane will likely be freed, greatly accelerating warming. Analysis of air bubbles trapped in ice sheets shows that methane is more abundant in the Earth’s atmosphere now than at any time during the past 400,000 years. Global average atmospheric concentrations of methane have increased from approximately 700 parts per billion by volume in 1750 — at the time of the Industrial Revolution — to roughly 1,800 parts per billion in 1998. Levels of the gas in the atmosphere had held steady since 1998, then suddenly spiked in 2007, when National Oceanic and Atmospheric Administration studies show they increased by 27 million tons. Researchers confirmed this finding in October 2008; they believe that unusually warm conditions over Siberia affected methane levels in the Northern Hemisphere by increasing the amount of methane produced by bacteria in Siberian wetlands. Scientists are not sure whether the methane spike signals the beginning of a long-term, massive release or is a one-time blip, but say that given methane’s power to warm the climate, even a small increase is cause for concern. Unleashing the methane reservoir could potentially warm the Earth tens of degrees; a violent opening of this “methane ice” (also known as clathrates), according to some scientists, may have triggered a catastrophic climate change and reorganization of the ocean and atmosphere around 635 million years ago. The U.S. Environmental Protection Agency estimates that methane volumes equivalent to taking 90 million cars and light trucks off the road could be achieved globally by 2020 at a cost benefit or at no cost. In the United States alone, that would be the equivalent of taking more than 12 million cars and light trucks off the road. And the EPA analysis doesn’t even include the value of significant air-quality and health benefits that would accompany methane reductions: Studies have found that reducing global methane emissions by 20 percent would save 370,000 lives between 2010 and 2030, due to the decrease in ozone-related cardiovascular, respiratory, and other health impacts. EPA may be underestimating available no-cost and low-cost methane mitigation options, but even its conservative analysis clearly demonstrates the opportunities available in methane control. Enormous reductions can be achieved with currently available technology, while mandatory greenhouse gas regulation would speed the development and deployment of new technology and mitigation options, making much deeper reductions feasible in the near future. But the key is rapid action: Methane needs to be dealt with immediately through strong regulation to sharply restrict emissions. Because of the urgency of the problem, and the need to address methane now, longer-term attempts to address the crisis will not be sufficient. |HOME / DONATE NOW / SIGN UP FOR E-NETWORK / CONTACT US / PHOTO USE /|

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- Download PDF 3 Answers | Add Yours Because DNA is a double helix with two chains that are complementary, either side may act as a template for its replication. DNA is the only molecule that can copy itself. Its subunits are called nucleotides. These contain a sugar--deoxyribose, a phosphate group and one of four bases--adenine, guanine, cytosine or thymine. These bases pair up with their complement on the adjacent chain. The rules are A pairs with T and C pairs with G. During replication, the hydrogen bonds between complementary bases are overcome and either chain can be replicated. Free nucleotides attach to exposed bases. For example, if the DNA code reads: A, T, C, G, then a complementary chain will be produced with the basesT, A, G, C. Because of this property, life can go on. DNA can be replicated for daughter cells produced during mitosis and also, for gamete production during meiosis. DNA molecules have the unique ability to self-replicate. This ability is important in cell division, which occurs during growing, development, and replacement of damaged cells. As DNA contains genetic information, it is necessary for DNA to replicate before division, otherwise the cells would not function correctly. DNA is also a very stable molecule, it is hard to break apart without the help of enzymes, etc. This is important because DNA has to store the information to code for every single protein produced by the organism. If DNA were to fall apart, the cells would not function. We’ve answered 324,323 questions. We can answer yours, too.Ask a question

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Only about 20 light years away – practically in our backyard – an Earth-like planet was recently discovered by Stéphane Udry of Geneva and collaborators , using a technique that measures a star's tiny shifts in velocity towards and away from us Those tiny shifts are caused by a planet, and their timing tells us the period of the planet's orbit. For the Earth, that period would be one year. For this planet, that period is about 13 days. With such a short period, it's possible to collect data for many repeating orbits, and build confidence in the signal over time. If astronomers know the mass of the central star (usually from the spectral type of the star), then the amplitude of the velocity shift reveals the minimum mass of the planet. In this case, that mass is about 5 times the Earth's mass. Then, if you assume what the planet is made out of (and therefore guess its average density), you can estimate its volume, and therefore its size. So if it's made out of rock, the planet is about 1.5 times the size of Earth; if it is made out of water – which is not as dense as rock – it would be bigger. With such a short period, you might guess that the planet is very close to its central star and you'd be right. But this central star is not like the Sun. It is much cooler and it is less massive than the Sun. So it's possible this planet might be habitable. You might be wondering how anybody knows the temperature of the planet if they can't see the planet at all. It's easy to estimate the temperature of an airless rock of some size orbiting a star at a constant distance. The main assumption there is a guess at how reflective the rock is. From the size of the rock, its distance from the star, the radiation emitted by the star, and the reflectivity of the rock, scientists can estimate the equilibrium temperature. The equilibrium temperature is that temperature that the rock settles on, once the radiation that is absorbed by the rock equals the radiation that is emitted by it. The calculation gets a little bit more complicated once you include an atmosphere with greenhouse gases. Such gas allows optical light to pass through to the ground, but absorbs the infrared light emitted by the planet. That gas thus slows the speed with which the planet can radiate energy back into space, and thereby increases the equilibrium temperature of the planet. It's this greenhouse effect that allows the Earth to have a quite lovely average equilibrium temperature as opposed to below freezing; it's this same greenhouse effect ("set to 11" as a certain pseudo-heavy metal band would say) that transforms Venus's surface into an unsurvivable vision of hell So the crucial question of whether this new planet has the right conditions for liquid water hinges on its atmosphere. If it utterly lacks an atmosphere, the surface can't maintain liquid water no matter what temperature it is. Like the surface of the Moon, the lack of vapour pressure would cause any liquid water to quickly disperse. If it has an atmosphere, the question is whether the greenhouse gases are just enough to allow a hospitably warm surface like Earth. Excessive greenhouse gases result in a Venus. The main excitement is that this planet is the smallest planet discovered to date, and that this planet, because of its distance from its central star, has the potential to have the right conditions for liquid water. But I wouldn't hop on my interstellar spaceship just yet. One hundred trillion miles is a long way to go just to find out there's nothing there to drink.Megan Donahue, Michigan State University astrophysicist (Illustration: ESO) Labels: atmosphere, exoplanet, extrasolar, Gliese 581, greenhouse effect, radial velocity

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Graphene, a material made of a single layer of carbon atoms, is being touted as the material that could change how electronics are made. But it’s difficult to make graphene in forms needed for electronics. Now, researchers from Stanford University have found a new method of making graphene by chemically converting DNA templates into flat sheets of carbon, potentially overcoming that limitation. In graphene, carbon atoms are arranged in a hexagonal structure. This symmetrical structure is a good conductor of electricity. Shape it into ribbons narrower than 10 nanometres (billionths of a metre), though, and it can act as a semiconductor. If we can mass produce these thin ribbons, they could be used to build very small and efficient circuits and transistors, potentially making electronics cheaper, faster, and smaller. Many approaches to making narrow graphene ribbons have been reported in recent years. These vary from unzipping carbon nanotubes (a form of carbon that exists as tiny tubes), to burning away a layer of graphene in the presence of a mask bearing the right shape. Approaches in which the graphene is made via chemical reactions from simple starting materials have also been described. All of these approaches have had limited success in producing long ribbons that are less than 10nm wide. The key innovation of the Stanford team was to use DNA as a template. DNA is readily available from natural sources and is easily manipulated into different shapes, from the narrow ribbons required here to elaborate 3D architectures dubbed “DNA origami.” It also binds readily to metal ions such as the copper catalyst used to convert methane to graphene. Zhenan Bao and colleagues report these findings in Nature Communications. Using a process called molecular combing, they extended bacterial DNA across a silicon wafer, forming the required shape. The team made both simple ribbons and overlapping crosses—in principle complex circuits could be designed in this way. Once the DNA is in place, it is soaked in a solution of copper nitrate and heated to 800-1000 °C in the presence of methane and hydrogen gases. This starts a chemical reaction that leaves behind a graphene-like material in the shape of the DNA template. The non-carbon portions of DNA and the copper, which acts as a catalyst, evaporate in the furnace to give a pure product. Most importantly, the process forms ribbons less than 10nm wide. There are some limitations. The graphene ribbons are not pure, crystalline graphene. Around 15 percent of the ribbon consists of non-crystalline carbon that lacks the electrical properties of graphene. This reduces the ability of the ribbons to act as semiconductors; in effect, the ribbons have resistors built into them at random points. (To emphasize this, the authors described the ribbons as graphitic, meaning graphene-like.) Despite this, the researchers were able to build transistors out of the graphitic ribbons to demonstrate their potential applications. The presence of amorphous carbon means that high voltages must be applied to the ribbons before they will conduct. This reduces the useful lifetime of the graphitic material, and future work will certainly focus on modifying the chemistry so that it produces pure graphene. The mechanism by which the ribbons form during heating is not yet understood. Still, this work is a creative solution to an important problem. If the process can be refined to give large amounts of pure graphene ribbons, the next generation of electronic devices may well be a step closer.

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CCSS.Math.Content.4.MD.C.5 - Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: CCSS.Math.Content.4.MD.C.5.a - An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles. CCSS.Math.Content.4.MD.C.5.b - An angle that turns through n one-degree angles is said to have an angle measure of n degrees. Authors: National Governors Association Center for Best Practices, Council of Chief State School Officers Title: CCSS.Math.Content.4.MD.C.5 Recognize Angles As Geometric Shapes That Are Formed Wherever... Measurement and Data - 4th Grade Mathematics Common Core State Standards Publisher: National Governors Association Center for Best Practices, Council of Chief State School Officers, Washington D.C. Copyright Date: 2010 (Page last edited 05/13/2016) - Angle Measurement - Online quiz, adding adjacent angles. Given the size of a portion of the angle, what is the size of the other portion? - Angles - Online lesson on creating angles; types of angles; measurement. - Angles - Online matching game; match the explanation with the correct graphic angle. - Clocks and Angles - Online lesson and exercise using clocks to recognize angles. - How to Measure Angles - Online lesson introducing angles and measurement. - Learning about Angles - Use this online tool to demonstrate angles and measurements. - Line Plot Lesson Plan - Excellent lesson with interactives and engaging activities for students. - Measuring Angles - Practice lining up and reading a protractor while you measure a set of angles in a fun learning activity

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Problem : Calculate the net torque exerted by F 1 = 30 N and F 2 = 50 N in the figure below. You may assume that both forces act on a single rigid body. We begin be calculating the magnitude of each torque individually. Recall that τ = Fr sinθ . Thus τ 1 = (30)(1)sin 120 = 26.0 N-m and τ 2 = (50)(1)sin 30 = 25 N-m. As we can see from the figure, τ 1 acts counterclockwise while τ 2 acts clockwise. Thus the two torques act in opposite directions, and the net torque is thus 1 N-m in the counterclockwise direction. Two cylinders of the same mass and shape, one hollow and one solid, are set on a incline and allowed to roll down. Which cylinder will reach the bottom of the incline first? Why? Since both cylinders have the same shape, they will experience the same forces, and thus the same net torque. Recall that τ = Iα . Thus the cylinder with the smaller moment of inertia will accelerate more quickly down the incline. Think of each cylinder as a collection of particles. The average radius of a particle in the solid cylinder is smaller than the hollow one, as most of the mass of the hollow one is concentrated at a larger radius. Since moment of inertia varies with r 2 , it is clear that the solid cylinder will have a smaller moment of inertia, and thus a larger angular acceleration. The solid cylinder will reach the bottom of the incline first. A simple pendulum of mass m on a string of radius r is displaced from vertical by an angle θ , as shown below. What is the torque provided by gravity at that point? We begin by resolving the gravitational force into tangential and radial components, as shown below: See the last problem. What is the angular acceleration of the pendulum at that point? We already know the torque acting on the pendulum. Recall that τ = Iα . Thus, to find the angular acceleration we need to compute the moment of inertia of the pendulum. Fortunately, it is simple in this case. We can treat the mass on the pendulum as a single particle of mass m and radius r . Thus I = mr 2 . With this information we can solve for α : A revolving door is common in office buildings. What is the magnitude of the torque exerted on a revolving door of mass 100 kg if two people push on opposite sides of the door with a force of 50 N at a distance of 1 m from the axis of the door, as shown below? Also, the moment of inertia of a revolving door is given by I = . Find the resultant angular acceleration assuming no resistance. Although it looks like the forces are directed in opposite directions, and thus cancel out, we must remember that we are working with angular motion here. In fact, both forces point in the counterclockwise direction, and can be considered to have the same magnitude and direction. In addition, they are both perpendicular to the radial direction of the door, so the magnitude of the torque by each one is given by: τ = Fr = (50 N)(1 m) = 50 N-m. As we stated, the two forces act in the same direction, so the net torque is simply: τ = 100 N-m. Next we have to calculate angular acceleration. We already know the net torque and thus must find the moment of inertia. We are given the formula I = . We are given the mass, and from the figure we see that the radius is simply 1.5 m. Thus:

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- Define an operator in terms of Python programming. - Arrange the Python math operators in terms of their mathematical order of operations. - Define precedence in terms of Python operators. - Identify the Python equality, or comparison, operators. - Explain the difference between mathematical and boolean operators. - Compute three to five expressions using mathematical and boolean operators. - Draw a diagram of the various Python operators arranging them into distinct sets, specifically, boolean and mathematical. Operators work with one or more objects and can perform tasks such as math, comparison, and inspection. There are standard operators for arithmetic: Additionally, you can modify a named value and assign the output of an operator to the name in one line with inline assignment operators. >>> a_number = 1 >>> a_number += 1 >>> a_number 2 >>> a_number *= 8 >>> a_number 16 >>> a_number **= 2 >>> a_number 256 >>> a_number /= 2 >>> a_number 128 >>> a_number %= 3 >>> a_number 2 Comparison and Boolean The comparison operators compare the values of two values, variables, or expressions and return a boolean value (True or False). |<=||Less than or equal to||Boolean| |>=||Greater than or equal to||Boolean| |is not||different object||Boolean| |or||checks whether either A or B is True||Boolean| |and||returns True if A and B are True|| Examples of comparison operators follow. >>> 1 == 1 True >>> 2 > 1 True >>> 3 <= 4 True >>> 2 + 5 >= 14 / 2 True >>> (2 + 5 >= 14/2) and (2 <= 4) True >>> a = 5 >>> b = 9 >>> a != b True

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The Polish state temporarily ceased to exist when the territories of the once-powerful Kingdom of Poland were divided among Prussia, Austria, and Russia in three partitions of 1772, 1793, and 1795. Nationalist aspirations were not extinguished, and determined factions within Poland's former frontiers and in exile waged a persistent struggle for the restoration of independence in the century and a quarter that followed. Polish support was sought by both the Allies and the Central Powers in World War I. The Allies announced as one of their war aims the reestablishment of an independent Polish state. The Germans, occupying the country with the Austrians after driving out the Russian armies, set up a Polish Government on 5 November 1916 in an effort to gain the favor of the nationalists. The Allied offer had a greater appeal to the Poles, and the Polish National Committee in Paris, the strongest exile group, under Ignace Paderewski, identified itself with the Allies. The Polish Republic was proclaimed by nationalist leaders at Warsaw on 3 November 1918, as it became obvious that the Central Powers were about to suffer a military collapse. Executive power was assumed by the Regency Council, the government organized two years before by the German occupation authorities. The Regency Council promptly called upon Jozef Pilsudski, the military leader who had led Polish troops in Austrian service against the Russians, to assume the leadership of the new republic. Pilsudski was invested with the powers of a military dictator and immediately invited Paderewski and other Polish leaders in exile to return. A coalition government was formed under Paderewski on 17 January 1919. The new Polish state commenced its existence in the midst of ruin and poverty. Its territory had been the scene of heavy fighting between the Central Powers and the Russians in the opening stages of World War I, and the German and Austrian occupation forces had systematically exploited the country in the several years that followed. The end of the war found Poland's factories destroyed or idle, its livestock decimated, and the nation's economy in a state of chaos. Reconstruction and economic recovery in Poland were to take far longer than was the case with most other World War I participants. Poland's northwestern and western borders were fixed by the Treaty of Versailles between Germany and the Allies on 28 June 1919, and its southern frontier by the Treaty of St. Germain between the Allies and Austria-Hungary on 10 September 1919. The Treaty of Riga (Latvia), 18 March 1921, ended a successful campaign by the newly established state against Soviet Russia and determined Poland's eastern and northeastern frontiers. The territorial clauses of the treaty between Germany and the Allies provided Poland with a land corridor to the Baltic Sea and the site of the future port of Gdynia, at the expense of the prewar Reich. This arrangement isolated the province of East Prussia from Germany, disrupted much of the Reich's economy, and placed thousands of Germans in the Corridor within the borders of the new Polish state. Danzig, a major port at the mouth of the Vistula and populated almost completely by Germans, was made a free city, with a League of Nations commissioner and its own elected legislature. Poland was permitted to control Danzig's customs, to represent the Free City in foreign affairs, and to keep a small military force in the harbor area. A plebiscite was to be held to determine the frontier in parts of Upper Silesia, but the Poles secured several of the more desirable areas by force in a sudden rising on 18 August 1919. Despite heated German protests, these areas were incorporated into Poland. Later plebiscites divided other areas along lines corresponding to the wishes of the local population. A Polish-French treaty of alliance on 19 February 1921 was designed to maintain the territorial arrangements that had been made and to provide France with an eastern counterweight to future German expansion. The German attack on Poland precipitated World War II, making the Polish campaign one of particular significance to the student of the 1939^5 conflict. The lessons learned by the German Army in its operations in Poland were put to use in the later campaigns against the western Allies, the Balkan states, and the Soviet Union. Poland also formed the testing ground for new theories on the use of armored forces and close air support of ground troops. The complete destruction of the Polish state and the removal of Poland from the map of eastern Europe were grim portents of the fate of the vanquished in the new concept of total war. |Join the GlobalSecurity.org mailing list|

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Finding the Key Parts of All Hyperbolas Part of the Pre-Calculus Workbook For Dummies Cheat Sheet A hyperbola is the set of all points in the plane such that the difference of the distances from two fixed points (the foci) is a positive constant. Hyperbolas always come in two parts, and each one is a perfect mirror reflection of the other. There are horizontal and vertical hyperbolas, but regardless of how the hyperbola opens, you always find the following parts: The center is at the point (h, v). The graph on both sides gets closer and closer to two diagonal lines known as asymptotes. The equation of the hyperbola, regardless of whether it's horizontal or vertical, gives you two values: a and b. These help you draw a box, and when you draw the diagonals of this box, you find the asymptotes. There are two axes of symmetry: The one passing through the vertices is called the transverse axis. The distance from the center along the transverse axis to the vertex is represented by a. The one perpendicular to the transverse axis through the center is called the conjugate axis. The distance along the conjugate axis from the center to the edge of the box that determines the asymptotes is represented by b. a and b have no relationship; a can be less than, greater than, or equal to b. You can find the foci by using the equation f 2 = a2 + b2.

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