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Exponents are shorthand for repeated multiplication of the same thing by itself, and it's power refers to the number of times it is multiplied. In this chapter we will learn about the basics of exponents and introduce the concept of powers with negative exponents. In this topic we will learn about negative exponents, exponent properties involving quotients, zero, non-negative, and fractional exponents. We will also solve some exercises to have a better understanding of this topic. We have already studied laws of exponents in grade 7 but there powers of exponents used to be positive. Here we will study about the laws of exponents with negative powers. The laws which are applicable to positive powers of exponents shall be applicable on negative powers of exponents as well.

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Molecules—like the ones that make up your body—are just collections of atoms held together by chemical bonds. In many ways, they're a lot like Tinkertoy® building projects. In fact, if you take organic chemistry, you’ll most likely buy a model set that looks suspiciously similar to Tinkertoys®: Ball-and-stick model of the atom proline made using a modeling kit. Just as you can put Tinkertoy® wheels together in different ways using different stick connectors, you can also put atoms together in a different ways by forming different sets of chemical bonds. The process of reorganizing atoms by breaking one set of chemical bonds and forming a new set is known as a chemical reaction. Chemical reactions occur when chemical bonds between atoms are formed or broken. The substances that go into a chemical reaction are called the reactants, and the substances produced at the end of the reaction are known as the products. An arrow is drawn between the reactants and products to indicate the direction of the chemical reaction, though a chemical reaction is not always a "one-way street," as we'll explore further in the next section. For example, the reaction for breakdown of hydrogen peroxide (H2H, start subscript, 2, end subscriptO2O, start subscript, 2, end subscript) into water and oxygen can be written as: 2H22, H, start subscript, 2, end subscriptO2(hydrogen peroxide)O, start subscript, 2, end subscript, left parenthesis, h, y, d, r, o, g, e, n, space, p, e, r, o, x, i, d, e, right parenthesis→right arrow2H2O(water)2, H, start subscript, 2, end subscript, O, left parenthesis, w, a, t, e, r, right parenthesis + O2(oxygen)O, start subscript, 2, end subscript, left parenthesis, o, x, y, g, e, n, right parenthesis In this example hydrogen peroxide is our reactant, and it gets broken down into water and oxygen, our products. The atoms that started out in hydrogen peroxide molecules are rearranged to form water molecules (H2OH, start subscript, 2, end subscript, O) and oxygen molecules (O2O, start subscript, 2, end subscript). You may have noticed extra numbers in the chemical equation above: the 22s in front of hydrogen peroxide and water. These numbers are called coefficients, and they tell us how many of each molecule participate in the reaction. They must be included in order to make our equation balanced, meaning that the number of atoms of each element is the same on the two sides of the equation. Equations must be balanced to reflect the law of conservation of matter, which states that no atoms are created or destroyed over the course of a normal chemical reaction. You can learn more about balancing reactions in the balancing chemical equations tutorial. Reversibility and equilibrium Some chemical reactions simply run in one direction until the reactants are used up. These reactions are said to be irreversible. Other reactions, however, are classified as reversible. Reversible reactions can go in both the forward and backward directions. In a reversible reaction, reactants turn into products, but products also turn back into reactants. In fact, both the forward reaction and its opposite will take place at the same time. This back and forth continues until a certain relative balance between reactants and products is reached—a state called equilibrium. At equilibrium, the forward and backward reactions are still happening, but the relative concentrations of products and reactants no longer change. Each reaction has its own characteristic equilibrium point, which we can describe with a number called the equilibrium constant. To learn where the equilibrium constant comes from and how to calculate it for a specific reaction, check out the equilibrium topic. When a reaction is classified as reversible, it is usually written with paired forward and backward arrows to show it can go both ways. For example, in human blood, excess hydrogen ions (H+H, start superscript, plus, end superscript) bind to bicarbonate ions (HCO3H, C, O, start subscript, 3, end subscript−start superscript, minus, end superscript), forming carbonic acid (H2H, start subscript, 2, end subscriptCO3C, O, start subscript, 3, end subscript): HCO3H, C, O, start subscript, 3, end subscript−start superscript, minus, end superscript + H+H, start superscript, plus, end superscript⇌H2H, start subscript, 2, end subscriptCO3C, O, start subscript, 3, end subscript Since this is a reversible reaction, if carbonic acid were added to the system, some of it would be turned into bicarbonate and hydrogen ions to restore equilibrium. In fact, this buffer system plays a key role in keeping your blood pH stable and healthy. Raven, P. H., Johnson, G. B., Mason, K. A., Losos, J. B., and Singer, S. R. (2014). The nature of molecules and properties of water. In Biology (10th ed., AP ed., pp. 17-30). New York, NY: McGraw-Hill. Reece, J. B., Urry, L. A., Cain, M. L., Wasserman, S. A., Minorsky, P. V., and Jackson, R. B. (2011). Chemical reactions make and break chemical bonds. In Campbell Biology (10th ed., pp. 40-41). San Francisco, CA: Pearson.

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Graphing with Coordinates in a PowerPoint Presentation This slideshow lesson is very animated with a flow-through technique. It was made for my 7th Grade class, but can be used for lower grades. This lesson was one of a chapter that was used as a review for all previous grades. The lesson teaches how to plot on a coordinate plane and use a T-table to solve problems. This lesson has a unique way of remembering how to plot a point. The visual in this lesson is well worth it. The students will never again get the x and y coordinate mixed up. The presentation has 57 slides with TONS of whiteboard practice. Use as many or as few of the problems to help your students learn each concept. For more PowerPoint lessons & materials visit: Students often get lost in multi-step math problems. This PowerPoint lesson is unique because it uses a flow-through technique that helps to eliminate confusion and guide the student through the problem. The lesson highlights each step of the problem as the teacher is discussing it, and then animates it to the next step within the lesson. Every step of every problem is shown, even the minor or seemingly insignificant steps. A helpful color-coding technique engages the students and guides them through the problem. Twice as many examples are provided, compared to a standard textbook. All lessons have a real-world example to aid the students in visualizing a practical application of the concept. Common Core Standard: Graph points on the coordinate plane to solve real-world and mathematical problems 1. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Please note that these PowerPoints are NOT EDITABLE. They WILL NOT work with Google Slides. You will need the PowerPoint software. If you need an alternative version because your country uses different measurements, units, slight wording adjustment for language differences, or a slide reordering just ask. This resource is for one teacher only. You may not upload this resource to the internet in any form. Additional teachers must purchase their own license. If you are a coach, principal or district interested in purchasing several licenses, please contact me for a district-wide quote at firstname.lastname@example.org. This product may not be uploaded to the internet in any form, including classroom/personal websites or network drives. *This lesson contains 16 problems. Each problem in this lesson uses several pages in order to achieve the animated flow-through technique.

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Astronomers learn about the universe by deciphering messages carried by the radiation from extraterrestrial bodies. Electromagnetic radiation travels across the vacuum of space at 300,000 kilometers per second. The light we see with our eyes is just one example of this radiation. Light spread out in order of wavelength is a visible spectrum of the object. However, there are also wavelengths far too short (too blue) to see, and wavelengths far too long (too red) to see. The entire electromagnetic spectrum covers a tremendous wavelength range, from gamma rays the size of an atomic nucleus to radio waves many meters long. Electromagnetic radiation can be described as a wave or a particle, depending on the kind of interaction it has with matter. Waves have a wavelength, or typical distance between peaks. Their frequency is a measure of the number of peaks that pass per second. Wavelength and frequency are inversely related. Radiation can be considered either as a particle, or a photon, whose energy is proportional to its frequency. Atoms absorb and release energy in the form of photons — these discrete units of matter and energy mean that the microscopic world is "grainy." Most of what we know about the universe depends on the ways that matter and radiation interact with each other. Objects in space reveal their nature by the radiation they emit. The smooth thermal spectrum has a peak wavelength that indicates the temperature. In addition to a smooth spectrum, any hot gas has sharp spectral features. These sharp lines appear because the electrons around an atomic nucleus can only inhabit certain fixed energy levels. When electrons change their energy level, they emit a spectral line of a specific wavelength. Each element and compound has its own lines and bands. The spectral lines act like a fingerprint that helps us figure out what a hot object is made of. Even though scientists make very accurate measurements, the microscopic world is fundamentally "fuzzy." There is a limit to the precision with which scientists can measure microscopic quantities, a concept expressed in the Heisenberg uncertainty principle. This means that subatomic particles cannot have their positions and motions measured with certainty, leading to a situation that requires us to recognize that both our data and our knowledge of the physical universe may be limited. This limitation is not apparent when large objects like people or planets or stars. Telescopes are devices that improve on the light-gathering power of the eye and allow astronomers to resolve finer details of an astronomical target. Thus we can see objects much fainter than those visible to the unaided eye. The light-gathering power and the resolution of a telescope increase with increasing aperture. Most modern telescopes are reflectors. There is currently a surge in the construction of large telescopes on mountaintop sites around the world. We have a dozen telescopes with apertures of 8 meters and larger, and several in the range 20-30 meters are planned. Since optical detectors are almost perfectly efficient, astronomers need a larger collecting area to see deeper into the universe. The technique of interferometry gives astronomers far better resolution than can be achieved with a single telescope. Other telescopes have been placed in orbit to give ultra-sharp optical images and to detect long and short wavelengths that cannot penetrate the Earth's atmosphere. Perhaps the most exciting revolution is the peeling back of the electromagnetic spectrum, revealing for the first time the invisible universe.

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As every natural language has a basic character set, computer languages also have a character set, rules to define words. Words are used to form statements. These, in turn, are used to write the programs. Computer programs usually work with different types of data and need a way to store the values being used. These values can be numbers or characters. C language has two ways of storing number values—variables and constants—with many options for each. Constants and variables are the fundamental elements of each program. Simply speaking, a program is nothing else than defining them and manipulating them. A variable is a data storage location that has a value that can change during program execution. In contrast, a constant has a fixed value that can’t change. This tutorial is concerned with the basic elements used to construct simple C program statements. These elements include the C character set, identifiers and keywords, data types, constants, variables and arrays, declaration and naming conventions of variables.

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Ks2 Grid Method Multiplication Worksheet Posted on Sep 05, 2018 by Maria Rodriquez Ks2 Grid Method Multiplication Worksheet ~ welcome to our site, this is images about ks2 grid method multiplication worksheet posted by Maria Rodriquez in category on Sep 05, 2018. You can also find other images like preschool worksheet, kindergarten worksheet, first grade worksheet, second grade worksheet, third grade worksheet, fourth grade worksheet, fifth grade worksheet, middle school worksheet, high school worksheet. Please scroll down to view more images... You almost certainly know already that ks2 grid method multiplication worksheet is one of the top topics over the internet these days. Depending on the data we acquired from google adwords, ks2 grid method multiplication worksheet has a lot of search in google web engine. We think that ks2 grid method multiplication worksheet offer fresh thoughts or references for readers. We have discovered numerous sources about ks2 grid method multiplication worksheet but we feel this is the best. I hope you would also consider our opinion. This picture has been posted by our team and is in category tags page. You are able to get this image by hitting the save link or right click on the graphic and select save. We sincerely hope that whatever we give to you could be useful. If you want, you can share this content for your companion, loved ones, community, or you can also book mark this page. Note : Any content, trademark/s, or other material that may be found on the Best Free Printable Worksheets website that is not Best Free Printable Worksheets property remains the copyright of its respective owner/s. In no way does Best Free Printable Worksheets claim ownership or responsibility for such items, and you should seek legal consent for any use of such materials from its owner. Keywords for Ks2 Grid Method Multiplication Worksheet : Related Posts of Ks2 Grid Method Multiplication Worksheet :

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How Do We Measure Up? This How Do We Measure Up? lesson plan also includes: - Join to access all included materials Fifth graders define the difference between area and perimeter. Students determine the area and perimeter of objects around the school setting. 3 Views 0 Downloads - Activities & Projects - Graphics & Images - Handouts & References - Lab Resources - Learning Games - Lesson Plans - Primary Sources - Printables & Templates - Professional Documents - Study Guides - Graphic Organizers - Writing Prompts - Constructed Response Items - AP Test Preps - Lesson Planet Articles - Interactive Whiteboards - All Resource Types - Show All See similar resources: "How Do You Measure Up?" Measurement Patterns Students explore measurement units by completing a math worksheet. For this human body measurement lesson, students read the book How Do You Measure Up and practice measuring their limbs, head and other parts of their body with standard... 4th - 5th Math Convert Measurements to Solve Weight Problems How do you break down and solve a word problem that involves converting weight measurements? And how can that help decide how many strawberries are needed in fruit salad? That's the focus of this lesson. A handy review of metric units... 6 mins 3rd - 5th Math CCSS: Designed Convert Measurements to Solve Volume Problems The second of five videos on solving word problems involving measurement data conversion focuses on converting a larger unit to a smaller unit in a real-life word problem. A review of milliliters versus liters starts the discussion,... 7 mins 3rd - 5th Math CCSS: Designed Measure Quarter and Three-Quarter Rotations Measuring angles is a mysterious task. What do those degrees mean? A clock is used to show what each angle looks like on a circle as the hands move around to mark time. The lesson explains that rays are just like the hands of a clock,... 5 mins 4th - 5th Math CCSS: Designed Represent Fractional Distance Measurement Quantities Using Diagrams The first lesson in a series of five, the lesson supports learners in discovering new strategies for finding fractional distances by using diagrams with measurement scales. After a review of fractions and diagrams, the common mistake of... 8 mins 3rd - 5th Math CCSS: Designed

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What Is Gneiss? Gneiss (from German; pronounced “nice”) is a foliated, high-grade metamorphic rock with a characteristic, banded texture. This texture can be clearly seen in the image below. Gneiss can form from many different rocks, and it may contain many different minerals. How is Gneiss Formed? Like all metamorphic rocks, gneiss forms when an already existing rock (called a “parent rock” or “protolith”) undergoes a process called metamorphism. This process transforms rocks by subjecting them to heat and/or pressure, and the amount of heat and pressure determines what kind of metamorphic rock is formed. To form gneiss, both very high levels of temperature and pressure are required; these conditions will likely be on the order of several kilobars (one kilobar = one thousand atmospheres) and several hundreds of degrees Celsius. These conditions most commonly occur deep within continental crust where the weight of overlying rock creates high pressure and heat from radioactive decay creates high temperatures. When metamorphism occurs, the intense pressure and heat that drive the metamorphism cause minerals from the protolith to recrystallize into new minerals. This process, called recrystallization, occurs because minerals are stable only at certain temperatures and pressures. As a result, the minerals in the protolith transform into new materials that are stable at the conditions occurring during metamorphism. Then, once the rock cools, the minerals are “locked in” to their new states. In the case of gneiss, however, the minerals do not merely recrystallize; they also reorient themselves into separate, easily visible bands perpendicular to the direction of stress. This phenomenon, known as foliation, causes the characteristic gneissic banding. (Note that there are other types of foliation as well.) Due to the intense conditions necessary to form gneiss, this rock is considered a “high-grade” metamorphic rock. The only metamorphic rock with a higher grade is called migmatite; this rock forms when a gneiss undergoes partial melting due to even higher temperatures and pressures. Other metamorphic rocks such as slate, phyllite, and schist all have lower grades of metamorphism than gneiss, because they endure lower temperatures and pressures during metamorphism. Common Minerals in Gneiss The different colored bands in gneiss contain different minerals; the lighter bands often contain felsic minerals like feldspars and quartz, whereas the darker bands usually contain mafic minerals like amphiboles, hornblende, and biotite. The minerals present in a given gneiss depend heavily upon the protolith itself, and two different samples of gneiss may contain entirely different sets of minerals despite both exhibiting gneissic banding. Types of Gneiss and Protoliths Many different protoliths can produce gneiss if the appropriate conditions are met during metamorphism. If the protolith is an igneous rock like granite, then the resultant gneiss is called an orthogneiss; see the image below. Conversely, if the protolith is a sedimentary rock, then the end product will be called a paragneiss. How to Identify Gneiss The easiest way to identify gneiss is to look for the banding on the surface of the rock. These bands typically exhibit alternating layers of light and dark minerals, and they may vary up to a few millimeters in width. Identifying gneiss can sometime prove troublesome, however, because metamorphism occurs on a spectrum, which causes some metamorphic rocks to exhibit characteristics of multiple types of metamorphic rocks. That different metamorphic rocks can sometimes form and be found right next to one another further complicates identifying gneiss or other metamorphic rocks. Locations Where Gneiss is Found Because gneiss forms only at high temperatures and pressures, and these conditions are typically found deep within the Earth, most of the gneiss on the Earth’s surface has been brought to the surface via plate tectonics and associated mechanisms and/or revealed due to erosion and weathering. Gneiss may be found worldwide in rock outcrops, and even regions that have no exposed metamorphic rock outcrops may still have gneiss on the surface due to glaciers transporting gneiss from another area and dropping it on the surface in glacial till. Uses of Gneiss Gneiss can sometimes contain gemstone-quality stones such as garnet, and it may also be used as a building material or provide decorative stoneware for landscaping. Some of the oldest rocks known on Earth are gneisses; scientists have found gneiss from Greenland that is over 3.5 billion year old. These rocks and other metamorphic rocks are therefore important for interpreting Earth history. In addition, gneiss can reveal information about past tectonic events due to the unique conditions needed to form gneiss. If gneiss is exposed in a rock outcrop, for example, then that’s a good clue that that region was at one point buried deep underground.

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About This Chapter Making Inferences & Justifying Conclusions in Math - Chapter Summary In statistics, it's important to have the ability to make inferences and justify conclusions. This chapter helps you sharpen these skills through bite-sized and entertaining lessons. Work through the chapter to review methods for interpreting expected values, comparing random variables, finding sample variance and much more. By the end of the chapter, you should be equipped to: - Draw conclusions from sample surveys - Differentiate between observational studies and experiments - Assess the difference between statistics and parameters - Explain the process of estimating sample data parameters - Use equations for finding sample mean and variance - Compare types of random variables - Find/interpret the expected values of continuous random variables - Develop continuous probability distributions Each lesson comes with a short quiz that's designed to reinforce the information you study. Take these quizzes along with the chapter exam to master these mathematical concepts. You can watch the lessons online using your computer or mobile device, and you also have the option of printing our word-for-word lesson transcripts. Finally, if you have any questions, you can use the chapter's convenient Ask the Expert feature. 1. Drawing Conclusions from Sample Surveys In this lesson, we look at a fictitious survey and show how to draw conclusions based on several criteria. Being able to discern the criteria of a good survey allows valid conclusions to follow the statistical analysis. 2. Experiments vs Observational Studies: Definition, Differences & Examples There are different ways to collect data for research. In this lesson, you will learn about collecting data through observational studies and experiments and the differences between each. 3. Defining the Difference between Parameters & Statistics Using data to describe information can be tricky. The first step is knowing the difference between populations and samples, and then parameters and statistics. 4. Estimating a Parameter from Sample Data: Process & Examples One of the most useful things we can do with data is use it to describe a population. Learn how in this lesson as we discuss the concepts of parameters and samples. 5. Sample Mean & Variance: Definition, Equations & Examples Sample mean and variance are both important statistics that can you can use to make predictions about a population. In this lesson, learn how to calculate these important values. 6. Random Variables: Definition, Types & Examples This lesson defines the term random variables in the context of probability. You'll learn about certain properties of random variables and the different types of random variables. 7. Finding & Interpreting the Expected Value of a Continuous Random Variable How can you find the expected value of something like height distributions? This lesson explains how to find and interpret the expected value of a continuous random variable. 8. Developing Continuous Probability Distributions Theoretically & Finding Expected Values What is an expected value? How can you tell how many time you should expect a coin to land on heads out of several flips? This lesson will show you the answers to both questions! Earning College Credit Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level. To learn more, visit our Earning Credit Page Transferring credit to the school of your choice Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you. Other chapters within the TASC Mathematics: Prep and Practice course - TASC Math: Real Numbers - TASC Math: Complex and Imaginary Numbers Review - Intro to Algebraic Expressions - Intro to Algebraic Equations - TASC Math: Exponents and Exponential Expressions - Overview of Square Roots - TASC Math: Radical Expressions - TASC Math: Functions - TASC Math: Graphing and Functions - Overview of Sequences - TASC Math: Inequalities - TASC Math: Algebraic Distribution - TASC Math: Linear Equations - TASC Math: Factoring - TASC Math: Quadratic Equations - TASC Math: Graphing and Factoring Quadratic Equations - TASC Math: Properties of Polynomial Functions - TASC Math: Rational Expressions - TASC Math: Measurement - Lines, Angles & Arcs - Shapes in Geometry - Volume & Surface Area - TASC Math: Calculations, Ratios, Percent & Proportions - TASC Math: Data, Statistics, and Probability - TASC Mathematics Flashcards

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Series Circuit Example. In the show circuit below, two light bulbs are connected in series. No nodes are necessary inside this circuit to show the bulbs connecting to each other and also into the battery since single wires are linking straight to each other. Nodes are just placed if three or more wires are connected. Component References. Components at a circuit should always have references, also called reference designators, utilized to identify the components in the circuit. This allows the components to easily be referenced in text or a component list. The base terminals of the bulbs are linked to each other and to the negative terminal of the battery life, because the next node shows these connections. Circuit Symbols and Physical Components. Each electronic or electric element is represented by a symbol as may be seen in this simple circuit structure. Lines used to join the symbols represent conductors or wires. Each symbol represents a physical element that may look as follows. A part list is now able to refer to these components. Circuit diagrams or schematic diagrams show electric connections of wires or conductors by using a node as shown in the picture below. A node is a filled circle or scatter. After three or more lines touch each other or cross each other along with a node is put at the junction, this represents the wires or lines being connected at the point. The easiest way for beginners to continue learning how to read circuit diagrams is to follow the course and build the circuits from every tutorial. Parallel Circuit Example In the circuit below, two light bulbs are connected in parallel to a battery power source. It can be seen that the upper terminals of both light bulbs are connected together and into the positive terminal of the battery. We know this because the three terminals or link points have a node where they intersect. Circuit or schematic diagrams contain symbols representing bodily components and lines representing cables or electric conductors. In order to learn how to read a circuit diagram, it's vital to learn what the design symbol of a part appears like. It is also necessary to understand how the components are linked together in the circuit. If lines or wires cross each other and there is no node, as shown in the base of the aforementioned image, the cables aren't electrically connected. In this case the cables are crossing each other without linking, like two insulated wires put you on top of another. Fundamental components for this tutorial comprise a LED, resistor and battery that can be found at the newcomer's component reference. Battery and Light Bulb Circuit. Probably the simplest circuit which may be drawn is one that you might have noticed in a school science course: a battery attached to a light bulb as shown under. When beginning to learn to read digital circuit diagrams, it is essential to learn exactly what the schematic symbol looks like to get many different digital components. The Start Electronics Currently electronics class for beginners is made up of a collection of tutorials for beginners in electronics. Observing the path explains how to examine basic digital circuit diagrams while constructing the circuits on electronic breadboard. The course comprises a record of basic electronic elements using their schematic symbols in which novices can learn exactly what the physical elements and their logos look like. Physical Circuit. The physical circuit for the above circuit diagram may look something similar to the image below, though a more practical physical circuit would have a light bulb holder and clamps that connect with the battery terminals. A light bulb holder could have screw terminals to attach the cables to, and a socket to screw the light bulb in to. Because there could be more than one battery or light bulb in a circuit, reference designators will typically always end with a number, e.g. BAT1 and L1 as shown in the circuit below. A second light bulb at the circuit would then have the reference designator L2. This articles demonstrates how to read circuit diagrams for beginners in electronics. A drawing of an electrical or electrical circuit is also known as a circuit diagram, but could also be called a schematic diagram, or merely schematic. Listed below are overall circuit diagram rules. Following a four part introduction, the first tutorial at the electronics course shows the circuit diagram of a simple LED and resistor circuit and also the way to construct it upon breadboard. Specifying Components. Typically the actual battery kind and bulb type would be specified in a component list that communicates the circuit diagram. More info on the bulb and battery type could also be contained in the circuit as text. For example, the battery could be defined as a 12.8V 90Ah Lithium battery, plus a 9V PM9 battery. The light bulb may be specified as a 12V 5W incandescent bulb, or 9V 0.5W flashlight bulb.

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Or download our app "Guided Lessons by Education.com" on your device's app store. EL Support Lesson Students will be able to read high-frequency rhyming sight words. Students will be able to identify and verbally share sight words and rhyming words in a fiction story using a picture sort. - Introduce the lesson by telling students that today they will be practising their reading and listening skills as they learn all about rhyming words and sight words. Building academic language - Display the images of rhyming words and read each pair aloud. - Ask students if they notice anything special about each word pair. - Explain that the words rhyme by saying, "When two or more words end in the same sound, they rhyme" - Put the definition of rhyme on the board for students to reference. - Tell the class that now you will play a rhyming word game. Explain that you will say two words aloud. If the words rhyme, students should stand up. If they don't rhyme, they should stay seated. - Say several rhyming and non-rhyming words aloud. Have students practise identifying which words rhyme. - Ask students to turn to a partner, say one word aloud, and have the partner share a word that rhymes. For example, "Can, what word rhymes with can?" - Repeat with several more words. - Write the word "in" on the board or chart paper in large print - Explain that this word is called a sight word by saying, "A sight word is a word that we see often when we read and should memorize so that we can read it nice and fast." - Tell the class that you will now read a story that has the word "in" and also some rhyming words for them to practise! - Read aloud the book, Bear Snores To the class. - As you read, pause to notice the word "in." Encourage the class to give a thumbs up when they hear this sight word - Stop reading when you read aloud two rhyming words. Ask the students to say the words aloud with you and listen for the part that sounds the same (e.g., howl/growl). Additional EL adaptations - Provide students with rhyming picture word cards to match with a partner to practise identifying rhyming words. - Ask students to come up with their own rhyming word pairs using words from the classroom word wall. Formative Assessment of Academic Language(10 minutes) - Pass out the Rhyming Puzzles worksheets to each student and have them complete with a partner. - Ask students to say each rhyming pair aloud to their partner, and assess whether students were able to accurately match each of the rhyming words. Review and closing(5 minutes) - Have students complete the Read and Draw Sight Words: In worksheet as an exit ticket. - Say the word "in" aloud. Model thinking aloud to find a rhyming word, such as "tin." - Ask students to think of words that rhyme with "in", and turn and talk to a partner to share their words.

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Verbs typically express actions or activities (like fallen, gehen, schreiben, stehlen), processes (like gelingen, sterben, wachsen) or states (like bleiben, leben, wohnen). They constitute the core of the sentence and are usually accompanied by one or more noun phrases, i.e. the subject and the other complements of the verb: Subject Verb Complement(s) Der Lehrer Ihre Freundin Die Mutter Der alte Mann redet unterrichtet gibt wartet Unsinn die deutsche Sprache ihrer Tochter die Mappe auf seine Frau In German, verbs change their form (typically adding endings or changing the vowel) to express various grammatical ideas like tense, e.g. present and past; mood, e.g. the imperative and the subjunctive; and person and number, e.g. du (second person singular), wir (fi rst person plural). These are known as the grammatical categories of the verb. All the different forms of each verb make up its conjugation. This chapter gives details on the conjugation of regular and irregular verbs in German, as follows: • Basic principles of the conjugation of verbs in German (section 12.1) • The conjugation of the simple present and past tenses and the imperative (section 12.2) • The conjugation of the compound tenses: future and perfect (section 12.3) • The conjugation of the passive (section 12.4) • The conjugation of the subjunctive (section 12.5) The forms of all strong and irregular verbs are given in Table 12.12, at the end of the chapter.

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2 Chapter GoalsLearn about the normal, bell-shaped, or Gaussian distribution.How probabilities are found.How probabilities are represented.How normal distributions are used in the real world. 3 6.1: Normal Probability Distributions The normal probability distribution is the most important distribution in all of statistics.Many continuous random variables have normal or approximately normal distributions.Need to learn how to describe a normal probability distribution. 4 Normal Probability Distribution: 1. A continuous random variable. 2. Description involves two functions:a. A function to determine the ordinates of the graph picturing the distribution.b. A function to determine probabilities.3. Normal probability distribution function:This is the function for the normal (bell-shaped) curve.4. The probability that x lies in some interval is the area under the curve. 6 Illustration of probabilities for a normal distribution: 7 Note:1. The definite integral is a calculus topic.2. We will use a table to find probabilities for normal distributions.3. We will learn how to compute probabilities for one special normal distribution: the standard normal distribution.4. Transform all other normal probability questions to this special distribution.5. Recall the empirical rule: the percentages that lie within certain intervals about the mean come from the normal probability distribution.6. We need to refine the empirical rule to be able to find the percentage that lies between any two numbers. 8 Percentage, proportion, and probability: 1. Basically the same concepts.2. Percentage (30%) is usually used when talking about a proportion (3/10) of a population.3. Probability is usually used when talking about the chance that the next individual item will possess a certain property.4. Area is the graphic representation of all three when we draw a picture to illustrate the situation. 9 6.2: The Standard Normal Distribution There are infinitely many normal probability distributions.They are all related to the standard normal distribution.The standard normal distribution is the normal distribution of the standard variable z (the z-score). 10 Properties of the Standard Normal Distribution: 1. The total area under the normal curve is equal to 1.2. The distribution is mounded and symmetric; it extends indefinitely in both directions, approaching but never touching the horizontal axis.3. The distribution has a mean of 0 and a standard deviation of 1.4. The mean divides the area in half, 0.50 on each side.5. Nearly all the area is between z = and z = 3.00.Note:1. Table 3, Appendix B lists the probabilities associated with the intervals from the mean (0) to a specific value of z.2. Probabilities of other intervals are found using the table entries, addition, subtraction, and the properties above. 11 Table 3, Appendix B entries: The table contains the area under the standard normal curve between 0 and a specific value of z. 12 Example: Find the area under the standard normal curve between z = 0 and z = 1.45. A portion of Table 3: 13 Example: Find the area under the normal curve to the right of z = 1 Example: Find the area under the normal curve to the right of z = 1.45; P(z > 1.45).Area asked for 14 Example: Find the area to the left of z = 1.45; P(z < 1.45). 15 Note:1. The addition and subtraction used in the previous examples are correct because the “areas” represent mutually exclusive events.2. The symmetry of the normal distribution is a key factor in determining probabilities associated with values below (to the left of) the mean. For example: the area between the mean and z = is exactly the same as the area between the mean and z =3. When finding normal distribution probabilities, a sketch is always helpful. 16 Example: Find the area between the mean (z = 0) and z = -1.26. Area asked forArea from table0.3962 17 Example: Find the area to the left of -.98; P(z < -.98). Area asked forArea from table0.3365 18 Example: Find the area between z = -2.3 and z = 1.8. 19 Example: Find the area between z = -1.4 and z = -.5. Area asked for 20 Note: The normal distribution table may also be used to determine a z-score if we are given the area (to work backwards).Example: What is the z-score associated with the 85th percentile?implies 21 Solution:In Table 3 Appendix B, find the “area” entry that is closest toThe area entry closest to isThe z-score that corresponds to this area is 1.04.The 85th percentile in a normal distribution is 1.04. 22 Example: What z-scores bound the middle 90% of a normal distribution? implies 23 Solution:The 90% is split into two equal parts by the mean.Find the area in Table 3 closest tois exactly half way between andTherefore, z = 1.645z = and z = bound the middle 90% of a normal distribution. 24 6.3: Applications of Normal Distributions Apply the techniques learned for the z distribution to all normal distributions.Start with a probability question in terms of x-values.Convert, or transform, the question into an equivalent probability statement involving z-values. 25 Standardization:Suppose x is a normal random variable with mean m and standard deviation s.The random variablehas a standard normal distribution. 26 Example: A bottling machine is adjusted to fill bottles with a mean of 32.0 oz of soda and standard deviation of Assume the amount of fill is normally distributed and a bottle is selected at random.1. Find the probability the bottle contains between 32 oz and oz.2. Find the probability the bottle contains more than oz. 29 Note:1. The normal table may be used to answer many kinds of questions involving a normal distribution.2. Often we need to find a cutoff point: a value of x such that there is a certain probability in a specified interval defined by x.Example: The waiting time x at a certain bank is approximately normally distributed with a mean of 3.7 minutes and a standard deviation of 1.4 minutes. The bank would like to claim that 95% of all customers are waited on by a teller within c minutes. Find the value of c that makes this statement true. 31 Example: A radar unit is used to measure the speed of automobiles on an expressway during rush-hour traffic. The speeds of individual automobiles are normally distributed with a mean of 62 mph. Find the standard deviation of all speeds if 3% of the automobiles travel faster than 72 mph.Illustration: 33 Notation:If x is a normal random variable with mean m and standard deviation s, this is often denoted: x ~ N(m, s).Example: Suppose x is a normal random variable with m = 35 and s = 6. A convenient notation to identify this random variable is: x ~ N(35, 6). 34 6.4: Notation z-score used throughout statistics in a variety of ways. Need convenient notation to indicate the area under the standard normal distribution.z(a) is the token, or algebraic name, for the z-score (point on the z axis) such that there is a of the area (probability) to the right of z(a). 35 Illustrations:z(0.10) represents the value of z such that the area to the right under the standard normal curve is 0.10z(0.80) represents the value of z such that the area to the right under the standard normal curve is 0.80 36 Example: Find the numerical value of z(0.10). Use Table 3: look for an area as close as possible toz(0.10) = 1.28Table shows this area (0.4000)0.10 (area information from notation) 37 Example: Find the numerical value of z(0.80). Use Table 3: look for an area as close as possible toz(0.80) = -.84Look for ; remember that z must be negative. 38 Note:The values of z that will be used regularly come from one of the following situations:1. The z-score such that there is a specified area in one tail of the normal distribution.2. The z-scores that bound a specified middle proportion of the normal distribution. 39 Example: Find the numerical value of z(0.99). Because of the symmetrical nature of the normal distribution, z(0.99) = -z(0.01).Using Table 3: z(0.99) = -2.330.01 40 Example: Find the z-scores that bound the middle 0 Example: Find the z-scores that bound the middle 0.99 of the normal distribution.Use Table 3: 41 6.5: Normal Approximation of the Binomial Recall: the binomial distribution is a probability distribution of the discrete random variable x, the number of successes observed in n repeated independent trials.Binomial probabilities can be reasonably estimated by using the normal probability distribution. 42 Background: Consider the distribution of the binomial variable x when n = 20 and p = 0.5. Histogram:The histogram may be approximated by a normal curve. 43 Note:1. The normal curve has mean and standard deviation from the binomial distribution.2. Can approximate the area of the rectangles with the area under the normal curve.3. The approximation becomes more accurate as n becomes larger. 44 Two Problems:1. As p moves away from 0.5, the binomial distribution is less symmetric, less normal-looking.Solution: The normal distribution provides a reasonable approximation to a binomial probability distribution whenever the values of np and n(1 - p) both equal or exceed 5.2. The binomial distribution is discrete, and the normal distribution is continuous.Solution: Use the continuity correction factor. Add or subtract 0.5 to account for the width of each rectangle. 45 Example: Research indicates 40% of all students entering a certain university withdraw from a course during their first year. What is the probability that fewer than 650 of this year’s entering class of 1800 will withdraw from a class?Let x be the number of students that withdraw from a course during their first year.x has a binomial distribution: n = 1800, p = 0.4The probability function is given by:

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The scatter plots are used to compare variables. A comparison between variables is required when we need to define how much one variable is affected by another variable. In a scatterplot, the data is represented as a collection of points. Each point on the scatterplot defines the values of the two variables. One variable is selected for the vertical axis and other for the horizontal axis. In R, there are two ways of creating scatterplot, i.e., using plot() function and using the ggplot2 package's functions. There is the following syntax for creating scatterplot in R: Let's see an example to understand how we can construct a scatterplot using the plot function. In our example, we will use the dataset "mtcars", which is the predefined dataset available in the R environment. Scatterplot using ggplot2 In R, there is another way for creating scatterplot i.e. with the help of ggplot2 package. The ggplot2 package provides ggplot() and geom_point() function for creating a scatterplot. The ggplot() function takes a series of the input item. The first parameter is an input vector, and the second is the aes() function in which we add the x-axis and y-axis. Let's start understanding how the ggplot2 package is used with the help of an example where we have used the familiar dataset "mtcars". We can add more features and make a more attractive scatter plots also. Below are some examples in which different parameters are added. Example 1: Scatterplot with groups Example 2: Changes in axis Example 3: Scatterplot with fitted values Adding information to the graph Example 4: Adding title Example 5: Adding title with dynamic name Example 6: Adding a sub-title Example 7: Changing name of x-axis and y-axis Example 8: Adding theme

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Plotting functions and curvesLast revision: May 10, 2016 Plotting mathematical objects is both useful and beautiful. Today we will just scratch the surface of the vast area of mathematical computer graphics, but we hope to give you a hint of what it looks like. As our first task, we will try to plot a function. Imagine that you don’t know any maths, but you have a powerful calculator. How do you plot a function? You make up a table with a lot of points, and put all those points in a graph. OK, let us have a try. Let’s say we want to plot the $f(x)=\sin(x)$ function. Remember how to generate all $x$ values from 0 to 10 at once? That’s right, you just do x=0:10;. Now, you want to compute the sine of all those values and put the numbers on another vector. So, you do: y=sin(x);. Next, you Octave the command to plot the result: Of course, the command plot, takes two arguments: the x values and the vector of values, and plots them. But you can see that the plot is quite coarse and ugly. How to improve them? Right: give more points!! 0:0.1:10 means all numbers from 0 to 10, with steps of size 0.1, so we get 0, 0.1, 0.2, ... 1, 1.1, 1.2, ... 9.8, 9.9, 10. Thus, many more points. The plot is much smoother and nice. You can also do several plots on the same screen very easily: Remember that some functions require a dot in order to be properly evaluated for a vector. For example, 1./x. Thus, if we want to plot $f(x)=1/(1+x^2)$ in the range $x \in [-10,10]$, we have to do: plot command is only useful to plot in cartesian coordinates. But, if we have a vector of $\theta$ values and another of $R$ values, we can convert them to cartesian coordinates with our usual expressions: So, let us try an example. Let’s plot $R(\theta)=\theta $. We will give a wide range for $\theta$, in order to be sure that we catch it all. Now, for something more beautiful, we can try a polar rose, $R(\theta) = \cos(5\theta/12)$: - Plot the polynomial $y=1-x^2$ and the gaussian $y=\exp(-x^2)$. - Draw an ellipse in polar coordinates, with semiaxes $a=2$ and $b=5$. - A particle follows a trajectory given by the equations $x(t)=\sin(t)$, $y(t)=\sin(2t)$. Start getting a vector for your $t$ values, using t=0:0.1:20;, and use it to get an image of the trajectory.

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The Treaty of Guadalupe Hidalgo ended the U. S. -Mexican War. Signed on February 2, 1848, it is the oldest treaty still in force between the United States and Mexico. As a result of the treaty, the United States acquired more than 500,000 square miles of valuable territory and emerged as a world power in the late nineteenth century. Beyond territorial gains and losses, the treaty has been important in shaping the international and domestic histories of both Mexico and the United States. During the U. S. -Mexican War, U. S. eaders assumed an attitude of moral superiority in their negotiations of the treaty. They viewed the forcible incorporation of almost one-half of Mexico’s national territory as an event foreordained by providence, fulfilling Manifest Destiny to spread the benefits of U. S. democracy to the lesser peoples of the continent. Because of its military victory the United States virtually dictated the terms of settlement. The treaty established a pattern of political and military inequality between the two countries, and this lopsided relationship has stalked Mexican-U. S. relations ever since. Signing the treaty was only the beginning of the process; it still had to be approved by the congresses of both the United States and Mexico. No one could foresee how the Polk administration would receive a treaty negotiated by an unofficial agent; nor could they know the twists and turns of the Mexican political scene for the next few months. In both the U. S. and Mexican governments there was opposition to the treaty. In the United States, the northern abolitionists opposed the annexation of Mexican territory. In the Mexican congress, a sizable minority was in favor of continuing the fight. Nevertheless both countries ratified the document. The signing of the Treaty of Guadalupe Hidalgo marked the end of a war and the beginning of a lengthy U. S. political debate over slavery in the acquired territories, as well as continued conflict with Mexico over boundaries. In the Article V we can read that Mexico ceded to the United States Upper California and New Mexico, and included present-day Arizona and New Mexico and parts of Utah, Nevada, and Colorado. Mexico relinquished all claims to Texas and recognized the Rio Grande as the southern boundary with the United States—the border was seen by Mexico to be the Nueces River before the treaty. This is how United States obtained the territories mentioned above. In the Article VIII residents needed to decided to stay in territory that now belongs to United States or leave to Mexico, it is important to mention that this article is applied to was already established in this state, due to this article now Mexicans needed to decided whether they would stay in “United States” or go to the Republic of Mexico. They could leave and still keep their land or stay and choose on becoming a United States Citizen or keep their Mexican Nationality. The time to decide was a year if the year passed and residences have not taken a decision they will become United States citizens automatically. In the Article IX Mexicans who opted to become citizens will have the rights that were given by the United States to their citizens, they will have the liberty to practice any religion, and they will also be free to have property and total freedom. On the article X of course this was a legal document before been omitted by the US Senate use to grant lad made by Mexican Government in territories that before belonged to Mexico. This article was to protect Mexicans and provide them with land, we can say that this article was extinguished because it was a way to give Mexicans the right to own land in a territory that was being governed by the United States but was taken from Mexico. Later on Article X was replace by The Protocol of Queretaro. On 30 May 1848, when the two countries exchanged ratifications of the treaty of Guadalupe Hidalgo, they further negotiated a three-article protocol to explain the amendments. The first article stated that the original Article IX of the treaty, although replaced by Article III of the Treaty of Louisiana, would still confer the rights delineated in Article IX. The second article confirmed the legitimacy of land grants pursuant to Mexican law. The protocol further noted that said explanations had been accepted by the Mexican Minister of Foreign Affairs on behalf of the Mexican Government, and was signed in Santiago de Queretaro by A. H. Sevier, Nathan Clifford and Luis de la Rosa. The U. S. would later go on to ignore the protocol on the grounds that the U. S. representatives had over-reached their authority in agreeing to it. In my opinion The United States used all of these articles to satisfy their guilt for taking Mexican territory by war.

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Learn how ions are formed using the octet rule. Use the periodic table to predict the charge an atom will have when it becomes an ion. Learn whether an ion is a cation or anion and how to write the formula depending on what charge the ion has. How Ions Are Formed As we’ve learned before, atoms like to be stable. They feel most stable when their outer electron shells are full. They become full when they have eight electrons in them. This is called the octet rule, which says that atoms like to have full valence shells of eight electrons. Remember that the valence electrons are the electrons in the outermost energy shell of an atom. They get eight electrons by either borrowing some from or giving some to another atom. Let’s look at how this works. Atoms get eight valence electrons by giving electrons to another atom or by accepting electrons from another atom. How ions are formed Cations and Anions Atoms start out electrically neutral because they have the same number of negatively charged electrons and positively charged protons. An ion is an atom that has gained or lost one or more electrons and therefore has a negative or positive charge. A cation is an atom that has lost a valence electron and therefore has more positive protons than negative electrons, so it is positively charged. An anion is an atom that has gained a valence electron and is negatively charged. Take the element sodium, Na. With one valence electron, it is very unstable in its single form. It just has that one electron in its outermost shell, and it wants very badly to get rid of it. Look at chlorine (Cl) over there in Group VII. It has seven valence electrons in its outermost shell, and it badly wants to gain an electron to become full and happy. Sodium will easily lose that extra electron. When it does, it becomes unbalanced. It now has more protons than electrons, so it is positively charged. That is why it is usually written as Na+. Chlorine, on the other hand, has seven valence electrons and wants to add an electron to fill its outer shell. When it adds an electron, it becomes negatively charged (more electrons than protons) and forms an anion, usually written as Cl-. Atoms can gain or lose more than one electron at a time. If they do, they are written with the superscript of what they have gained or lost. Ca2+, for instance, has lost two electrons. I know it seems a bit confusing since it lost electrons but became positively charged. As you’ll remember, though, atoms are neutral to start with, so if they lose a negatively charged electron, they become positively charged. Ions are written with the superscript of the number of electrons they have gained or lost. Gaining and losing electrons Looking for a Similar Assignment? Order now and Get 10% Discount! Use Coupon Code “Newclient” The post Ions: Predicting Formation, Charge, and Formulas of Ions appeared first on Superb Professors.

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Worksheet For Class 3 Maths You’ll find a variety of examples and problems on a variety of subjects with solutions in third-grade math lessons. Students will learn math when playing third-grade math lessons because they are arranged in this way. In the third grade, every effort is made to incorporate new ideas into simple language, keeping in mind the child’s mental state so that he or she can easily understand them. Grade 3 Mathematics focuses on four-digit numbers, number comparisons, addition, subtraction, multiplication, and division, geometric shapes and figures, length measurement, mass measurement, power measurement, time measurement, money, fractional numbers, graphs, mental arithmetic, and shapes, among other topics. If the student follows our instructions, they will be able to develop their skills by working on third-grade math worksheets, which will help them perform higher on the third-grade math test. Class 3 Maths Questions – Maths Worksheet for Class 3 Also Read :-

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What Is an Election? ebook Guided Rd. Level R Interest Level 2-6 Teach students about the process of electing government leaders! This fun, meaningful Grade 3 nonfiction reader explains how elections work and ways that individuals can get involved in government. What Is an Election? - Describes the presidential election process with examples from United States history - Provides a short fiction piece related to the topic that will keep students invested - Explores major civics topics such as representative democracy and political parties - Includes a glossary, essential discussion questions, and a “Civics in Action” activity that will get students excited about elections and campaigns The road to the White House begins long before Election Day and involves lots of people, as students will learn in this engaging book! This teacher-approved product provides students with a close-up look at how leaders are elected and why voting is important. The book’s colorful images pair with a rich text to explain elections and civic duties in an easy-to-follow way. With its related fiction story, helpful index, and other key features, this book will excite third grade students while teaching them how to be informed participants of a representative democracy. In this section you can find reviews from our customers, or you can add your own review for this particular product. Customer reviews help other visitors to read feedback from users who have already purchased and are using TCM’s products.

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In an approach to classical physics, black holes are very large celestial objects - some hundreds of times the mass of the Sun - that occupy a very small space. Its gravitational field is so intense that not even the speed of light is greater than its escape velocity. With this, the light that enters a black hole can no longer come out, so that it cannot be observed by the usual techniques that analyze the light emitted or reflected by celestial objects. And what is escape velocity? We call escape velocity one whose intensity is sufficient for an object to “escape” from the action of the gravitational field. The escape velocity on the earth's surface is approximately 11.2 km / s; In order for an object to break free from the gravity of our planet, it must be launched faster than it. If a black hole cannot be seen, how is it detected? The observation of a black hole happens indirectly, because what can be seen are the effects that it has on nearby regions. Due to its huge gravitational field, other bodies tend to be attracted to it. By measuring how fast objects move toward you in neighboring regions, you can discover their mass. When a black hole absorbs matter from nearby bodies, it gets compressed, heats up significantly, and emits large amounts of X-ray radiation. The first detections of the black holes were made with sensors that captured this X-ray emission. Strong evidence has already been observed that there are supermassive black holes in the center of some spiral galaxies, including some scientists believe that there is one of these black holes in the center of our galaxy, the Milky Way.

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The compromise of 1850 comprised a number of acts, which were passed in 1850. The acts were passed by the United States Congress hoped to settle the strife, which existed between those people who supported slavery Northern parts and those who owned slaves in the southern parts of the United States of America. The compromise of 1850 was a major stepping stone in the history of the United States of America because it contains many forces and provisions. There are many speculations, which are made on how the country would be if the acts were not passed. The compromise of 1850 intended to stop the tension that existed in the between the northern and southern parts over the extended slavery in the Texas which was a new territory that had been gained by the United States of America in the Mexican war. Those people who were from the northern sides supported the compromise. This is because they claimed that the compromise would serve an opportunity to end slavery and reduce the influence of the southerners. However, those people from the southern parts of the country did not support it as they took it as a threat to thee political power, which they enjoyed. This was because the compromise would lead to admission of California in the union leading to equilibrium of the fifteen free and fifteen slave states. The compromise was an opportunity for America to expand its territories without much consideration of what kind of states they were (Rhodes, 2008). There was the Wilmot Proviso, which was amendment for a bill, which was related to the Mexican war, was supported by people from the northern parts. This is because it hoped to stop slavery from the northern parts and reduce the political power, which people from the south enjoyed. President Taylor was in support of this and proposed the admission of California and New Mexico to be states. This means that there would be two more states in the union. This caused an upset to the southerners. After his death, Millard Fillmore who succeeded him supported the compromise of 1850 completely. Henry clay, Webster Daniel and Stephen Douglas were the ones who led to the passage of the laws that were contained in the compromise. Douglas is credited for proposing that that the provisions be separated into components and a vote be held on each of the component. This is what added to the victory that the compromise gained. The opposition of the laws by the southerners was led by John C. Calhoun.Daniesl Webster plated a great role in making the compromise be accepted by the persuasive speeches which he gave supporting the laws (Hamilton & Holt, 2005). There are many more provisions which the compromise consisted other than the admission of a state to the union. One of the issues in the compromise, which was hot, was the issue of sovereignty. This is because the issue entailed that the residents were supposed to make their o9wn decision on matters, which pertained to them. Majority of the people supported the idea that the government was supposed to allow the residents of New Mexico and Utah make decisions for themselves whether they wanted to be a free state or a slave state. The other issue was of major concern in the compromise was the fugitive slave act which was urged by Clay. The acts stated that those who owned slaves had the right to capture and make those slaves who had fled to territory. However, the majority felt that the act was not of any help because it would be difficult for many of the slaveholders to incur the cost of a run away slave. The most controversial issue and the most important topic of the compromise of 1850 was whether California would be allowed to join the union of the free states, slave state or whether the decision was supposed to be decided by the popular sovereignty. The provisions were separated into separate votes, which made it possible for the majority to be for the compromise. Then it was signed as law by President Fillmore in 1850 (Waugh, 2003). Another aspect of compromise of 1850 was the provision of fugitive slave law, which was stringer. The compromise made it illegal not to return a slave who had run away to the south. It also provided that a suspected run away slave would be tried by one judge but not by jury. There was away that the judges were compensated more money by making a decision that a slave was guilty. Therefore, this law acted as one way of discouraging people from harboring slaves. However, the compromise of 1850 was not just a debate, which ensued between, the North and the South but focused more over expansion and touched the issue of slavery. This compromise acted as a test of the strength of the United States of America. It showed that no matter what the circumstances it is possible for a goal to be attained by a common man if there is the desire and persistence (Rhodes, 2008). Hamilton, H. & Holt, M. (2005) Prologue to conflict: the crisis and compromise of 1850, Kentucky, University Press of Kentucky. Rhodes, J. (2008) History of the United States from the Compromise of 1850, Volume 1, New York, BiblioBazaar, LLC. Waugh, J. (2003) On the brink of Civil War: the Compromise of 1850 and how it changed the course of American history, USA, Rowman & Littlefield.

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Explore the following two-dimensional shapes. Think about these questions as you explore the shapes: - What are some similarities and differences? - How could you sort these shapes? - What do you notice about the vertices? How are they similar or different? Record your ideas using a method of your choice. There are 5 shapes. They are: a square, which is a shape with 4 equal sides. A rectangle, which is a shape with 4 sides, two long and two shorter. A triangle, which is a shape with 3 equal sides. A pentagon, which is a shape with 5 sides. A hexagon, which is a shape with 6 sides. An angle is a shape formed by two rays (‘arms’ of an angle), or two line segments, that meet at a common endpoint (vertex). Angles are found when two lines intersect, or meet, at a common endpoint (vertex). For example, they are found on three-dimensional objects and two-dimensional shapes, wherever two line segments meet. Identifying the size of an angle involves finding the amount of rotation between two lines, segments, or rays that meet at a vertex. We measure the inside portion of the angle or the space between the two line segments. Therefore, the size of the angle is not affected by the length of its arms or by the direction the angle is placed. Explore the following examples, and decide if the angles are the same. If the angles are the same, select true; if the angles are different, select false. There are four different classifications of angles: right, acute, obtuse, and straight. Let’s explore each type of angle. Press on the tabs to learn more about angles. A right angle is an angle that measures 90 degrees. - A right angle is a quarter turn. - It is sometimes called a “square angle” because all angles of a square (or rectangle) are right. - If two lines meet at a right angle, the lines are perpendicular (meaning they intersect at 90 degrees). An acute angle measures between 0 degrees and 90 degrees. - This angle is smaller than a 90-degree angle. An obtuse angle is more than 90 degrees but less than 180 degrees. A straight angle measures 180 degrees. - This occurs when the rays lie opposite of each other. - This creates a straight line. Check your understanding by selecting the requested angle from each set or pair of angles. Sort the angles In this activity, you will sort ten angles by classifying them as: right, acute, obtuse, straight, or not an angle. You can record your thinking in the fillable and printable Sort the Angles Chart, or use a method of your choice. Important: Two of the "angles" in this activity are not actually angles! Can you identify the fake angles? As you explore the angles, remember these tips: - A turn greater than a right angle is an obtuse angle. - A turn less than a right angle is an acute angle. - A half turn, where the arms of the angle create a straight line, is a straight angle. Let’s begin! Explore the following angles, and decide on how to classify them. If you’d like, you can use the interactive protractor to measure the angles. Let’s explore a protractor! Try using it yourself, and ask for help if you need it! To rotate the protractor input the number of degrees you would like to rotate the protractor by and use the buttons to select the direction of rotation. Complete the fillable and printable Sort the Angles Chart to sort all the angles. You can also sort them in your notebook, or use another method of your choice. Explore the following five-pointed star. The star is made of five triangles and a pentagon in the centre. Answer the following questions about the star. Record your ideas in a notebook or a method of your choice. - How many angles does the pentagon have? What type(s) of angles are these? - There are 5 triangles. How many angles are there all together? How would you identify each angle? Are there any right angles? How do you know? - What might be the other angles? Are there any other spots where two lines meet at a vertex? Think about your learning Record your ideas to the following questions in a notebook or a method of your choice. - Why is it important to understand the different types of angles? - Why does the length of the rays not matter when exploring the size of the angle? As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence. Now, record your ideas using a voice recorder, speech-to-text, or writing tool. Press ‘Discover More’ to extend your skills.Discover More It’s time to play a game! You will now access Capital Clean Up to practice identifying different angles. You will need your teacher-created mPower usernames and password to access this activity.

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Numeracy - Stage 5 Add/Sub Term 4 Students are working towards being able to use a variety of part-whole strategies to add and subtract. • Use a range of additive strategies and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages. • Know counting sequences for whole numbers. • Know how many tenths, tens, hundreds, and thousands are in whole numbers. AA Equations and Expressions: • Record and interpret additive and simple multiplicative strategies, using words, diagrams, and symbols, with an understanding of equality. For detailed weekly planning please see folder in HB. Focus this term on knowledge - in particular decimals and understanding place value below zero

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As discussed in the first part of this chapter, a transistor is an excellent amplifier. The picture below shows an example. The input signal is connected to the amplifier via C1. C1 prevents a DC current flow in R1 and the input signal source, e.g. a microphone. DC currents may destroy the microphone (unless it's an electret; a type of microphone with a built-in amplifier). The characteristics of transistor T1 are: hFE=100 and VBE=0.6V. Assume we want to connect an end amplifier with a 10k input resistance to the OUT terminal. For maximum power transfer, the output resistance of our amplifier must be equal to the input resistance of the end amplifier. The output impedance of an amplifier is defined as vOUT/iOUT. In our case vOUT = vRC and iOUT = iRC. So the output impedance of this amplifier is vRC/iRC = RC. So RC = 10k. For stability reasons VRE must be VS/5. Since VS = 9V, VRE must be 1.8V. This means that the voltage at the OUT terminal can vary between 1.8 and 9V. So the maximum AC output voltage (vOUT,max) is 9-1.8=7.2Vtt. Obviously, this can only be arranged if the quiescent output voltage (when vIN=0) is exactly between 1.8 and 9V. This means VOUT=1.8+(9-1.8)/2=5.4V. We already know that RC=10k, so IC = (9-5.4V)/10k = 0.36mA. IE will also be 0.36mA, so RE=VRE/IE=1.8/0.36m=5k. VB = VBE + VRE. VBE is always 0.6V, so vRE = vB. (Remember: AC voltages and currents are written in lower case letters.) When C1 is large enough, vIN = vB = vRE. VOUT = VS - VRC = 9V - VRC => vOUT = -vRC. Knowing this, we can calculate the gain A of the amplifier, which is defined as: A = vOUT/vIN = -vRC/vRE=-(iC∙RC)/(iE∙RE). Since iC=iE (hFE is large enough to neglect iB), A=-(iC∙RC)/(iC∙RE) = -RC/RE. This means our amplifier's gain is -10k/5k =-2. VR1 = VS-VBE-VRE = 9-0.6-1.8 = 6.6V. IR1=IC/hFE=0.36mA/100=3.6μA. R1 = 6.6V/3.6μA = 1.8M. Unfortunately, transistors with the same type designation can have a wide range of hFE. For example, the hFE of a 2N3904 transistor ranges from 100 thru 300. The question is: will our amplifier still function properly if hFE = 300? Let's see... IB = (VS-VBE-VRE)/R1. VRE = IC∙RC = hFE∙IR1∙RE = hFE∙RE∙(VS-VBE-VRE)/R1 = hFE∙RE∙(VS-VBE)/R1 - hFE∙RE∙VRE/R1 => VRE+(hFE∙RE/R1)∙VRE = hFE∙RE∙(VS-VBE)/R1 => (1+300∙5k/1.8M)∙VRE = 300∙5k∙8.4/1.8M => 1.833∙VRE=7 => VRE = 7/1.833 = 3.8V. IB = (8.4-3.8)/1.8M = 2.6μA. IC = 300∙2.6μA = 0.767mA. However, IC,max = VS/(RC+RE)=9/15k=0.6mA. So hFE∙IB > IC,max, which means that the transistor is saturated and thus acts like a closed switch! Solution: add an extra resistor which makes VRE (and therefore IC) independent of hFE: Make sure IR1 >> IB => IR1≈IR2. Let's estimate proper values for R1 and R2. VR2 = VBE+VRE = 0.6+1.8V = 2.4V. VR1 = VS-VR2 = 9-2.4 = 6.6V. So R1:R2=6.6:2.4. E.g. R1=33k and R2=12k. In that case IR1(=IR2) = 6.6V/33k = 0.2mA, which is much larger than IB. As mentioned before, the voltage gain of this amplifier is just (-)2. In many cases that will not be enough. You can easily increase the gain by adding an extra resistor and capacitor as shown in the picture below: the most common transistor amplifier. Capacitor C2 shorts RE2 for AC voltages. So for DC signals, RE = RE1 + RE2, and for AC signals, RE = RE1. If RE1 = 500Ω and RE2 = 4.5k, we have an amplifier with the same characteristics as above, but the gain is 10k/500=20. The impedance of C2 must be much smaller than RE1: 1/(2∙π∙fmin∙C2) « RE1 => C2 » 1/(2∙π∙fmin∙RE1) where fmin is the lowest frequency the amplifier must be able to handle. For example: if fmin = 20Hz, C2 » 1/(2∙π∙20∙500) = 16μF. 47 or 100μF is a good choice. The AC input resistance of the amplifier is approximately R1//R2 = 8.8k. So the impedance of C1 must be much less than 8.8k => C1 » 1/(2∙π∙20∙8.8k) = 0.9μF. 10μF is a good choose. The positive terminal of C1 must be connected to the amplifier, unless the input signal's DC component is larger than 2.4V.

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led more than 300 other slaves to freedom. Her successful efforts earned her the nickname “Moses” and prompted southerners to offer large rewards for her capture.As you read, think about why Harriet Tubman risked her own freedom to help others gain theirs. Harriet Tubman (c. 1820–1913) about 1820. Her parents named her Araminta. As a young child, her masters red her out to other families for housework and child care. She never learned to read or write. As a teenager, Tubman worked the fields, which she preferred to domestic labor. She grew strong from working outdoors and learned to appreciate nature. She also experienced and witnessed cruelty, including the sale of two sisters who were carried off by slave traders to unknown destinations. In 1844, Araminta married a free African American named John Tubman. By law, she remained a slave, as would any children born to her. Tubman wondered about her own mother’s legal status. With the help of a lawyer, she learned that her master’s family had not honored a will setting her mother free at the age of 45. That betrayal and the prospect of being sold herself prompted Tubman to flee north in 1849. Following tradition, Tubman took a new name upon obtaining freedom: Harriet, her mother’s name. a niece and the niece’s children. In the spring of 1851, she rescued a brother and two other men. In the fall, she returned for her husband. Because he had taken a new wife, he refused to come with her. Tubman made her fourth trip on behalf of the Underground Railroad, leading two family members as well as nine strangers to freedom. In all, Tubman made 19 trips into the South, including an 1857 foray to bring her parents north. Rewards up to $40,000 were offered for her capture. Tubman didn’t just work on the Underground Railroad. She also helped abolitionist John Brown plan his raid on Harper’s Ferry. When the Civil War started, she followed Union soldiers to Virginia where she helped fugitive slaves encamped near Fort Monroe. She later assumed an official role as a spy and scout for the Union army in South Carolina. The information and guidance she provided helped Union soldiers conduct a raid that freed more than 750 slaves. After the war, Tubman helped emancipated African Americans who were orphaned, ill, disabled, or old. She also supported women’s suffrage until her death in 1913. In what ways did Tubman help enslaved What obstacles did Tubman face in her quest to help free other slaves? Make InferencesWhy do you think Tubman risked her own freedom to help others obtain theirs?

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Most people do not know of Elizabeth Cady Stanton, but much to people’s surprise, she was just as important in Women’s Rights Movement as Susan B. Anthony, if not more important. Elizabeth Cady Stanton helped to create remarkable strides in the Women's Rights. During her life, Elizabeth was an American suffragist, social activist, abolitionist, writer, lecturer, and chief philosopher of the women’s rights movement. She also organized the Seneca Falls Convention with Lucretia Mott whose aim was to obtain equal rights for women. During the Convention, Cady Stanton wrote the “Declaration of Sentiments” which declared that American women should have the same civil and political rights that American men had, including the right to vote. One thing Stanton emphasized in her declaration, was “that woman is man’s equal- was intended to be so by the Creator, and the highest good of the race demands that she should be recognized as such,” (Stanton 275). She believed women and men were equal under the eye of God and they should be treated so. Although women are Stanton’s “Declaration of Sentiments” was the first convention for women rights. Its purpose was to address the status of American women. Stanton felt that women were feeling they were getting shorted and disrespected of their rights. It was a list of resolutions to the problems dealing with their rights. She also included needs for women’s right to education, property, and vote. Women did not have many rights in the 19th century. They could not vote, serve on juries, if married could not keep wages or own property, and women could not get a good education. At a convention when two women tried to join a meeting they could not have a role in the proceeding. Later she made a convention that over 300 men and women showed up to. Then Stanton wrote the Declaration of Sediments that showed the rights they wanted. The Declaration of Sentiments, a document written by activists Elizabeth Cady Stanton and Lucrietia Mott, discusses injustices towards woman and the rights that have been withheld from them, such as voting and denied admittance into colleges. Stanton and Mott want readers, primarily men, to understand, to take action, and to fight against the opression that has been put on women of all ages, race and religion in the United States. Without the help of Stanton and Mott, womens rights may have been an overlooked issue yesterday and today, therefore, their message is incontestably crucial. To Stanton and Mott, women were created equal to men, and to further their declaration of this equality, they state that the rights that have been unfairly Men should have absolute rule over society. This was the mindset back when women's rights activists were considered rare and unorthodox. In A Declaration of Sentiments and Resolutions, Elizabeth Cady Stanton rejects the status quo and finds solutions to the overbearing problems she sees within society. A concept that has greatly been dreamt over throughout history has been challenged, by a woman. Elizabeth Cady Stanton exerts repetition, allusion, and pathos to express her opinions in favor of increasing women's rights. The Comparison of Two Declarations Thomas Jefferson and Elizabeth Cady Stanton fought for what they believed; which was being free and equal from unjust rule or unjust laws. In the “Declaration of Independence” By Thomas Jefferson; Jefferson writes about his concerns about current Government ruled by the King of Great Britain in the United States and proceeds to list conflicts that many people face in the United States due to the King’s unjust treatment towards its citizens. In the end of the essay he persuades that the United States should separate from the rule of Great Britain. In another essay written like the “Declaration of Independence” comes the “Declaration of Sentiments and Resolutions” by Elizabeth Cady Stanton, in Stanton’s essay she writes about issues that women face towards unjust laws. These laws were to prohibit and limit a women’s rights due to the fact they are married to their spouse; an example of these laws was “denied... the facilities for obtaining a through education” (149) to clarify this quotation women weren’t allowed to receive an education due to being married. Elizabeth Cady Stanton and Lucretia Mott meet at a National Anti-Slavery Convention, which influenced them to hold a Women’s Rights Convention. In 1848 they held a national women’s rights convention, known as the Seneca Falls Convention. At the convention Elizabeth Cady Stanton created the “Declaration of Sentiments”. Proposed in the Declaration was “that all men and women are created equal”. Over 300 men and women gathered at Seneca Falls for the convention and unanimously voted for women to have the right to have equal rights as men. In the 1970’s women were expected to stay at home and take care of the household. They were usually not expected to further their education, but instead take care of the children or tend to their husbands’ needs. In 1972 Judy Brady decided to let the readers of Ms. Magazine know how she felt about her “duties”. In her short essay, “Why I Want a Wife,” Brady uses pathos to connect and appeal to the reader’s emotions while explaining why she wants a wife. Stanton believed that a public protest of women’s right was the next step to get equality for women’s legal position. By this belief, Stanton tried to make a draft of “Declaration of Right and Sentiments”, which she modeled after the “Declaration of Independence”. In this declaration, Stanton demanded moral, economic and political equality for women. With her friends, Stanton was able to hold the first women’s right convention on 19-20 July 1848 at Stanton house in Seneca Falls, New York. That is why; the convention is called Seneca Falls Convention. However, for the women who were educated; like Elizabeth Cady Stanton, they used it to their advantage and brought women together by hosting a women’s right convention and had The Declaration of Sentiments signed by at least a hundred people who supported women’s Numerous women expressed their disapproval towards how they were denied their rights based on their gender, thus causing women to take a stand for their suffrage and rights. In a letter to her husband, Abigail Adams told him to “be more generous and favourable to [women] than [his] Anthony and Elizabeth Cady Stanton both are leading women’s rights activists during their time; their work influenced the American Peoples’ view on women. They founded one of the earliest pro-women’s rights movements in the country, which was essential in spreading feminism throughout America. Their lifelong battle against inequality to combat slavery and promote feminism through literary works like; 'The Revolution' and the Declaration of Sentiments speeches, succeeded after their death when women got the right to vote. Judy Brady’s “I Want A Wife” is a revolutionary piece that attempted to reveal the unequal roles men and women held in society. She goes through her prose by listing all the responsibilities her wife must have and the ways to make her happy. Brady’s whole article is satirizing these roles and is, in general, very sarcastic in her tone. She mocks a society that has given women an impossible standard and she starts with the deprivation of her education then continues with the role her wife should play in domestic ways, and then finishes with the expectations the sexual aspects of their relationship. I believe that Brady’s underlying message was and still is important for the development of equality in our nation. She speaks of all the contribution most of the women make and that men never appreciate, things that men think are the obligation of the wife. For instance, the writer says, “I want a wife who will keep my clothes clean, ironed, mended, replaced when need be, and who will see to it that my personal things are kept in their proper place so that I can find what I need the minute I need it” (Brady 503). This explains that, men want everything to be done by their wife, so they can only have whatever they need without doing some effort. Another example the author gives is that men want everything from women to be done, even that women have the same rights and obligations as men.

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Emotions are responses to a specific object, or in context to the situation. Emotions are the creators of mood. It can be anything that gives rise to feeling. Emotions are intense feelings that are directed at someone or something (Frijda, 1993). Etymologically the word emotion is derived from the Latin word "emovere" which means "to stir up" or "to exit." According to Charles G. Morris, "Emotion as "a complex affective experience that involves diffuse physiological changes and can be expressed overtly in characteristics behavior patterns." Natures and Characteristics of Emotion - Emotions are universal - prevalent in every living organism at all stages of development from infancy to old age. - Emotions are personal and thus differ from individual to individual. - Emotions have the quality of displacement. - The core of an emotion is feeling. - Every emotional experience involves many physical and physiological changes in the organism. - Emotion has motivational properties. - Emotional states are normally regarded as acute. - Emotions are regarded as intensely experienced states. - Emotional states are often behaviorally disorganized. - Emotion is accompanied by physiological correlates. - Emotion has cognitive appraisal. Types of Emotion (States of Emotion) - Positive emotion (love, curiosity, joy, happiness, laughter etc.) - Negative emotion (fear, anger, jealousy, guilt, anxiety, etc.) Functions of Emotion - Preparing us for action (a link between external events and behavioral responses). - Shaping our future behavior (act reinforcement). - Helping us to regulate social interaction (allow observers to better understand us). - Emotions help coordinate interpersonal relationships. - Emotions play an important role in the cultural functioning of keeping human societies together. - Emotions help us act quickly with minimal conscious awareness. - Emotions influence thoughts. - Emotional expressions provide incentives for desired social behavior.

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Skills to be acquired in this tutorial: To start learning how to symbolize sentences using predicate logic. There are many valid arguments which cannot be shown to be valid using sentential logic alone. For example, Beryl is a philosopher. All philosophers are wise. Beryl is wise. is valid. Yet if we try to analyse this at a propositional level we find that 'Beryl is a philosopher' is an atomic sentence (which might be symbolized by A) and 'All philosophers are wise' is also an atomic sentence, different from the first one (and so might be symbolized by B), and the conclusion 'Beryl is wise' is an atomic sentence different from the other two (and could be symbolized by C); so the apparent logical form of the argument, as judged by sentential logic, is A, B ∴ C which is an invalid form. Obviously what is needed here is a more careful look at the structure of the sentences which make up the argument. And predicate logic is the tool for this. The task of this second part of the course is to learn the symbolization techniques, the semantics, and the new rules of inference, for predicate logic. Then we will be in a position to make informed judgements about a wider range of arguments. In predicate logic, 'atomic' sentences are analysed at a finer level. A sentence like 'Beryl is wise' is not just something which is true or is false; rather it is something with a structure... there is a thing, Beryl, which has the property of being wise. To symbolize at predicate logic level, entities like Beryl are symbolized by constant terms which are lower case letters from the beginning of the alphabet ('b' would be fine for Beryl) and properties are symbolized by upper case letters ('W' would be fine for '..is wise'); and the two are put together by writing the property first followed by the individual it applies to. The result, using the conventions mentioned here, is Beryl is wise would be symbolized by Exercises to accompany Predicate Tutorial 1 It is usual to analyse an argument using only sentential logic or only predicate logic-- you do not mix up the two levels on one argument. We now move on to predicate logic... Exercise 1 (of 4): (*Note that English grammar is a context sensitive grammar and this means that no computer program can deal with it correctly in its entirety. This program makes simplifications and trims English down to a basic core 'near-English' which a computer can manage. For example, one simplification is not paying a lot of attention to having verbs agree properly with their subjects-- for the computer we write 'John goes' and 'John and Jill goes'. No doubt you will seized with a warm and humourous feeling when reading some of these sentences (all students of logic experience this at some time or another). The point of it is to convey how grammatical structure transforms into logical structure and the intermediate near-English helps in this . *) Exercise 2 (of 4): [This is a Video, click the Play button to view it..] Exercise 3 (of 4): Exercise 4 (of 4): If you decide to use the web application for the exercises you can launch it from here Deriver [Bergmann] — username 'logic' password 'logic'. Then either copy and paste the above formulas into the Journal or use the Deriver File Menu to Open Web Page with this address https://softoption.us/test/easyDeriver/CombinedExercisesEasyDBergmann.html . You may need to set some Preferences for this. - you can check that the parser is set to bergmann.

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Velocity is defined as the speed of an object in a certain direction. In many situations, to find velocity, we can use the equation v = s/t, where v equals velocity, s equals the total distance the object has moved from its initial position, and t equals time. However, this method only gives the "average" velocity value of the object over its displacement. Using calculus, you can calculate the velocity of an object at any point along its displacement. This value is called the "instant velocity" and can be calculated by the equation v = (ds)/(dt), or, in other words, is the derivative of the equation for the average velocity of the object. Method 1 of 3: Calculating Instantaneous Speed Step 1. Start with the equation for the velocity of the object's displacement To get the value of the instantaneous velocity of an object, we must first have an equation that describes its position (in terms of its displacement) at a given point in time. This means that the equation must have a variable s (which stands alone) on one side, and t on the other hand (but not necessarily standalone), like this: s = -1.5t2+10t+4 - In the equation, the variables are: Displacement = s. That is the distance traveled by the object from its starting point. For example, if an object travels 10 meters forward and 7 meters back, then the total distance traveled is 10 - 7 = 3 meters (not 10 + 7 = 17 meters). Time = t. This variable is self-explanatory. Usually expressed in seconds. # Take the derivative of the equation. The derivative of an equation is another equation that can give the slope value from a certain point. To find the derivative of the formula for the displacement of an object, derive the function using the following general rule: If y = a*x , Derivative = a*n*xn-1. This rule applies to any component that is on the "t" side of the equation. - In other words, start by descending the "t" side of the equation from left to right. Each time you reach the "t" value, subtract 1 from the exponent value and multiply the whole by the original exponent. Any constants (variables that do not contain "t") will be lost because they are multiplied by 0. This process is not as difficult as one might think, let's derive the equation in the step above as an example: s = -1.5t2+10t+4 (2)-1.5t(2-1)+ (1)10t1 - 1 + (0)4t0 -3t1 + 10t0 -3t + 10 Step 2. Replace the variable "s" with "ds/dt "To show that your new equation is the derivative of the previous equation, replace "s" with "ds/dt". Technically, this notation means "derivative of s with respect to t." A simpler way to understand this is that ds/dt is the value of the slope (slope) at any point in the first equation, for example, to determine the slope of a line drawn from the equation s = -1.5t2 + 10t + 4 at t = 5, we can plug the value "5" into the derivative equation. - In the example used, the first derivative equation would now look like this: ds/sec = -3t + 10 Step 3. Plug the value of t into the new equation to get the instantaneous velocity value Now that you have the derivative equation, it's easy to find the instantaneous velocity at any point. All you need to do is pick a value for t and plug it into your derivative equation. For example, if you want to find the instantaneous velocity at t = 5, you can replace the value of t with "5" in the derivative equation ds/dt = -3 + 10. Then solve the equation like this: ds/sec = -3t + 10 ds/sec = -3(5) + 10 ds/sec = -15 + 10 = -5 meters/second Note that the unit used above is "meter/second". Because what we calculate is displacement in meters and time in seconds (seconds) and velocity in general is displacement in a certain time, this unit is appropriate to use Method 2 of 3: Graphically Estimating Instantaneous Speed Step 1. Draw a graph of the object's displacement over time In the above section, the derivative is mentioned as the formula for finding the slope at a given point for the equation you are deriving. In fact, if you represent an object's displacement as a line on a graph, "the slope of the line at all points is equal to the value of its instantaneous velocity at that point." - To describe the displacement of an object, use x to represent time and y to represent displacement. Then draw the points, plugging the value of t into your equation, thus getting the value of s for your graph, mark t, s in the graph as (x, y). - Note that your graph can span below the x-axis. If the line representing the movement of your object reaches the bottom of the x-axis, then this means that the object has moved backwards from its initial position. In general, your graph won't reach the back of the y-axis - because we're not measuring the speed of an object moving past! Step 2. Select an adjacent point P and Q in the line To get the slope of the line at a point P, we can use a trick called "taking the limit." Taking the limit involves two points (P and Q, a point nearby) on the curved line and finding the slope of the line by connecting them many times until the distances P and Q get closer. - Let's say the object's displacement line contains the values (1, 3) and (4, 7). In this case, if we want to find the slope at the point (1, 3), we can determine (1, 3) = P and (4, 7) = Q. Step 3. Find the slope between P and Q The slope between P and Q is the difference in y values for P and Q along the x-axis value difference for P and Q. In other words, H = (yQ - yP)/(xQ - xP), where H is the slope between the two points. In our example, the value of the slope between P and Q is H = (yQ- yP)/(xQ- xP) H = (7 - 3)/(4 - 1) H = (4)/(3) = 1.33 Step 4. Repeat several times, moving Q closer to P Your goal is to reduce the distance between P and Q to resemble a dot. The closer the distance between P and Q, the closer the slope of the line at point P. Do this several times with the equation used as an example, using points (2, 4.8), (1.5, 3.95), and (1.25, 3.49) as Q and the starting point (1, 3) as P: Q = (2, 4.8): H = (4.8 - 3)/(2 - 1) H = (1.8)/(1) = 1.8 Q = (1.5, 3.95): H = (3.95 - 3)/(1.5 - 1) H = (.95)/(.5) = 1.9 Q = (1.25, 3.49): H = (3.49 - 3)/(1.25 - 1) H = (.49)/(.25) = 1.96 Step 5. Estimate the slope of the line for a very small distance As Q gets closer to P, H gets closer and closer to the value of the slope of the point P. Eventually, when it reaches a very small value, H equals the slope of P. Since we cannot measure or calculate very small distances, we can only estimate the slope on P after clear from the point we are trying. - In the example, as we move Q closer to P, we get values of 1.8, 1.9, and 1.96 for H. Since these numbers are close to 2, we can say that 2 is the approximate slope of P. - Remember that the slope at a given point on the line is equal to the derivative of the equation of the line. Since the line used shows the displacement of an object over time, and because as we saw in the previous section, the instantaneous velocity of an object is the derivative of its displacement at a given point, we can also state that "2 meters/second" is the approximate value of the instantaneous velocity at t = 1. Method 3 of 3: Sample Questions Step 1. Find the value of the instantaneous velocity at t = 4, from the displacement equation s = 5t3 - 3t2 +2t+9. This problem is the same as the example in the first part, except that this equation is a cube equation, not a power equation, so we can solve this problem in the same way. - First, we take the derivative of the equation: - Then, enter the value of t(4): s = 5t3- 3t2+2t+9 s = (3)5t(3 - 1) - (2)3t(2 - 1) + (1)2t(1 - 1) + (0)9t0 - 1 15t(2) - 6t(1) + 2t(0) 15t(2) - 6t + 2 s = 15t(2)- 6t + 2 15(4)(2)- 6(4) + 2 15(16) - 6(4) + 2 240 - 24 + 2 = 22 meters/second Step 2. Use a graphical estimate to find the instantaneous velocity at (1, 3) for the displacement equation s = 4t2 - t. For this problem, we will use (1, 3) as point P, but we must define another point adjacent to that point as point Q. Then we just need to determine the value of H and make an estimate. - First, find the value of Q first at t = 2, 1.5, 1.1 and 1.01. - Then, determine the value of H: - Since the value of H is very close to 7, we can state that 7 meters/secondis the approximate instantaneous velocity at (1, 3). s = 4t2- t t = 2: s = 4(2)2- (2) 4(4) - 2 = 16 - 2 = 14, so Q = (2, 14) t = 1.5: s = 4(1.5)2 - (1.5) 4(2.25) - 1.5 = 9 - 1.5 = 7.5, so Q = (1.5, 7.5) t = 1.1: s = 4(1.1)2 - (1.1) 4(1.21) - 1.1 = 4.84 - 1.1 = 3.74, so Q = (1.1, 3.74) t = 1.01: s = 4(1.01)2 - (1.01) 4(1.0201) - 1.01 = 4.0804 - 1.01 = 3.0704, so Q = (1.01, 3.0704) Q = (2, 14): H = (14 - 3)/(2 - 1) H = (11)/(1) = Q = (1.5, 7.5): H = (7.5 - 3)/(1.5 - 1) H = (4.5)/(.5) = Q = (1.1, 3.74): H = (3.74 - 3)/(1.1 - 1) H = (.74)/(.1) = 7.3 Q = (1.01, 3.0704): H = (3.0704 - 3)/(1.01 - 1) H = (.0704)/(.01) = 7.04 - To find the value of acceleration (change in velocity over time), use the method in the first section to obtain the derivative equation of the displacement function. Then create the derived equation again, this time from your derived equation. This will give you the equation to find the acceleration at any given time, all you have to do is enter your time value. - The equation relating the value of Y (displacement) to X (time) may be very simple, for example Y= 6x + 3. In this case, the slope value is constant, and there is no need to find the derivative to calculate it, where according to the equation of a straight line, Y = mx + b will equal 6. - Displacement is similar to distance, but has a direction, so displacement is a vector quantity, while distance is a scalar quantity. The displacement value can be negative, but the distance will always be positive.

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In this explainer, we will learn how to calculate the relative velocity of a particle with respect to another and how to calculate a relative velocity vector. When a particle moves in a straight line from one point, , to another, , we can describe its displacement using the vector If the particle moves from to in the time interval , then the velocity of this particle is given by This velocity is called the average velocity of the particle as it moves from to . If the velocity of the particle is constant, then this average velocity is equal to the velocity of the particle at any point during its motion. There are some situations where we may want to consider a different kind of velocity, which we call the relative velocity. Suppose you are sat on a train, looking out the window at a car driving in the opposite direction. Suppose also that the car is moving with a constant speed of 50 km/h and the train is moving with a constant speed of 80 km/h. Using this, we can say that the velocity of the train is 80 km/h, while the velocity of the car is km/h. However, since you are sat on the train, which is moving at 80 km/h, while observing the car move in the opposite direction, it will appear as though the car is moving faster than its speed of 50 km/h. This is due to relative velocities. Relative velocities tell us that movement is a relative concept, which means that it differs depending on the observer. In every case, while the viewer observes the movement of the other object, they consider themself to be at rest even if they are not. The velocity that the viewer observes the object moving at is not the actual velocity of the object, it is the relative velocity. Let us now consider how we can calculate relative velocities. Suppose that we have two bodies, and , such that the velocity of is and the velocity of is . A stationary observer would see the two bodies moving with their velocities and . Now, let us suppose the observer is sat on body , moving with velocity . The observer assumes that they are stationary, so when we are finding the relative velocity of , we will need to take this into consideration. First, suppose that , so is stationary. The observer is moving away from with velocity , so they will see move away from them with velocity . This is the relative velocity of with respect to , which we can call . In the case where , Next, we will consider when . Since the observer is still moving away with velocity , we will again need to take this into consideration. This time, we also have . To find the relative velocity of with respect to , we need to simply add to the we had before. This gives us that the relative velocity is Definition: Relative Velocity If bodies and are moving with velocities and , respectively, then we can say that the relative velocity of with respect to , , is given by and the relative velocity of with respect to , , is given by These formulas are given in terms of vectors, but they still hold for scalar quantities too. Let us look at an example that considers relative velocity purely in terms of the differences between velocity vectors. Example 1: Finding Relative Velocity Using Unit Vectors Fill in the blank: If and , then . The difference between and is given by Rearranging to find gives Substituting known values gives Now, let us look at another such example. Example 2: Finding Relative Velocity Using Unit Vectors If and , then the relative velocity . is a unit vector in some fixed direction. The difference between and is given by Substituting known values gives Let us consider an example where there is a context supplied, involving a body that measures the velocity of a second body relative to the first body. Example 3: Relative Speed of Bodies Moving in Opposite Directions A car is moving on a straight road at 84 km/h, and in the opposite direction, a motorbike is moving at 45 km/h. Suppose that the direction of the car is positive. Find the velocity of the motorbike relative to the car. Let be the velocity of the car and be the velocity of the motorbike. The direction of the car is positive; hence, and The velocity of the motorbike relative to the car is given by If two bodies move one-dimensionally in opposite directions, their speeds are added to determine the speed of either body relative to the other. Let us look at another example where this occurs. Example 4: Finding the Time to Complete a Journey Using Relative Velocities A ship was sailing with a uniform velocity directly toward a port that is 144 km away. A patrol aircraft passed over the ship traveling in the opposite direction at 366 km/h. When the aircraft measured the ship’s speed, it appeared to be traveling at 402 km/h. Determine the time required for the ship to reach the port. To determine the time required for the ship to reach the port, it is necessary to know the speed at which the ship approaches the port. The port is assumed to be stationary. The speed of the ship measured by the aircraft is 402 km/h. As the ship and aircraft travel in opposite directions, 402 km/h is the sum of their speeds. The speed of the aircraft is stated to be 366 km/h, so the speed of the ship is given by The time required to travel 144 km at a speed of 36 km/h is given by Let us consider an application of relative velocity in a context involving two bodies moving in the same direction. For two bodies moving in the same direction at speeds and , respectively, the speed of either body relative to the other, , is given by The trivially obvious case of this is the case corresponding to both bodies having the same speed, and hence the position of one body relative to the other is constant throughout the motion of the bodies. Example 5: Using Relative Velocity to Find the Length of a Train given the Time Taken by a Moving Object to Pass It A helicopter flew in a straight line at 234 km/h above a train moving in the same direction. It took the helicopter 21 seconds to travel the length of the train. Following this, the pilot halved the helicopter’s speed. Given that it took the train 14 seconds to pass the helicopter traveling at this speed, find the length of the train in metres. The most important thing to appreciate in this question is that because the helicopter and the train move in the same direction throughout, relative to the ground, their velocities have the same sign. The difference in their velocities is thus equal to the difference in their speeds, and the speed of the train relative to the helicopter (and vice versa), , is simply the difference between their speeds. In the first 21 seconds, the helicopter has a greater velocity relative to the ground than the train has, and in the 14 following seconds, the train has a greater velocity relative to the ground than the helicopter has. The change in the velocity of the helicopter between the first and the second time intervals is assumed to occur in negligible time. In each time interval, it is the case that where is the distance that the helicopter moves relative to the train (and vice versa), which is also the length of the train. The difference between the time intervals allows us to determine the velocity of the train. To simplify finding the length of the train in metres, the speed of the helicopter is converted to a speed in metres per second as follows: For the first time interval, For the second time interval, The length of the train remains constant, so the two terms can be equated to give This can be rearranged to determine the velocity of the train. Both sides of the equation can be divided by 14 to give The bracket can be expanded to give The rearrangement is then completed as follows: This value for can now be substituted into the equation for in either time interval. If the first of the time intervals is used, this gives us If the second of the time intervals is used, this gives us The length of the train is 273 metres. - If bodies and are moving with velocities and , respectively, then we can say that the relative velocity of with respect to , , is given by and the relative velocity of with respect to , , is given by - When finding relative velocities, it is useful to establish a sign convention for solving problems.

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GRE Permutation and Combination Concept and definition. The Factorial of a number (whole number only) is equal to the product of all the natural numbers up to that number. Factorial of n is written as n or n! and is read as factorial n. Hence 7! = 7 ×6 × 5×4 × 3 × 2 ×1 = 5040 5! = 5 ×4 ×3 ×2×1 = 120 n! = n× (n – 1)× (n – 2) × …… 3 × 2×1 1]0! = 1 (by definition) 3] 2! = 2 4] 3! = 6 5] 4! = 24 6] 5! = 120 7] 6! = 72 Permutation or combination is the number of ways in which an event occurred. AND denotes Multiplication , OR denotes Addition 1. We labelled each block with the number of ways, options, or alternatives available. 2. We multiply the number of blocks in each row. 3. In the case of code repetition always allow 4. The first digit in a code could be zero. 5. In Number, it is not possible to begin with zero. The question should specify whether there will be a repetition or not in the answer. 1. Permutations of n different things taken ‘r’ at a time is denoted by nPr and is given by nPr = (n! )/((n – r)! ) where r ≤ n. When to use it? When n distinct items present and r have to be selected and then arranged. Arrangements[permutation] – keywords – seating, sitting, sequence, order, alphabets, schedule, ranking, itinerary, codes, numbers, rows, lines, position. Order important – gives unique arrangements For e.g. A and B sitting on a chair can be AB or BA so these are two distinct arrangements It is basically selection followed by arrangement. So nPr =n!/(n-r)! The number of permutations when things are not all different. If there be n things, p of them of one kind, q of another kind, r of still another kind and so on, then the total number of permutations is given by (n! )/(p! q! r!..) Ex: In how many ways can you arrange the letters of the word Banana? 5 people A, B, C, D, E to be arranged in which A and B are together. 4 ! × 2! 5 people A, B, C, D, E to be arranged in which A and B are not together. 5! – 4! × 2! 1) No. of circular permutations of n things taken all at a time = (n – 1)! (2)Circular Permutations: ((n – 1) !)/(2 ) (if clockwise and anti-clockwise doesn’t matter ) No. of circular permutations of n different things taken r at a time = nPr/r - Number of combinations of n dissimilar things taken ‘r’ at a time is denoted by nCr & is given by nCr = (n! )/((n – r)! r!) where r ≤ n - Number of combinations of n different things taken r at a time in which q particular things will always occur is n – qCr – q - No. of combinations of n dissimilar things taken ‘r’ at a time in which ‘q’ particular things will never occur is n – qCr - nCr = nCn – r Combibation[Selection]- keywords – team, committee, balls, handshakes, matches, picking, random, select choose. Order not important – For example choosing A and B from a group of 3 or four alphabets. The order does not matter. India playing a match against Australia is the same as Australia playing against India.

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The first stars began to form around 400 million years after the birth of our universe. The so-called dark ages of the universe came to an end, and a new light-filled era began. More and more galaxies formed and served as factories for producing new stars, a process that peaked about 4 billion years after the Big Bang. Fortunately for astronomers, this bygone era can still be observed. It takes time for distant light to reach us, and our telescopes can detect light emitted by galaxies and stars billions of years ago (our universe is 13.8 billion years old). However, the details of this chapter in our universe’s history are murky because most of the stars that are forming are faint and obscured by dust. A new Caltech project called COMAP (CO Mapping Array Project) will provide a new look into this epoch of galaxy formation, helping to answer questions about what caused the universe’s rapid increase in star formation. “When looking at galaxies from this period, most instruments may only see the tip of an iceberg,” says Kieran Cleary, the project’s principal investigator and associate director of Caltech’s Owens Valley Radio Observatory (OVRO). “However, COMAP will see what is hidden beneath the surface.” The current phase of the project employs a 10.4-meter “Leighton” radio dish at OVRO to study the most common types of star-forming galaxies spread across space and time, including those that are too faint or obscured by dust to be seen in other ways. Radio observations reveal the raw material that stars are made of cold hydrogen gas. Because this gas is difficult to detect directly, COMAP measures bright radio signals from carbon monoxide (CO) gas, which is always present alongside hydrogen. The radio camera on COMAP is the most powerful ever built for detecting these radio signals. The project’s first scientific findings have just been published in seven papers in The Astrophysical Journal. COMAP set upper limits on how much cold gas must be present in galaxies at the epoch being studied, including those that are normally too faint and dusty to see, based on observations taken one year into a planned five-year survey. While the project has yet to directly detect the CO signal, these preliminary findings show that it is on track to do so by the end of the initial five-year survey, and that it will eventually paint the most comprehensive picture of the universe’s history of star formation. “In terms of the project’s future,” Cleary says, “we hope to use this technique to look further and further back in time.” “Beginning 4 billion years after the Big Bang, we will continue to push back in time until we reach the epoch of the first stars and galaxies, which was a couple of billion years earlier.” According to Anthony Readhead, co-principal investigator and Emeritus Robinson Professor of Astronomy, COMAP will witness not only the birth of stars and galaxies, but also their epic decline. “We’ll watch star formation as it rises and falls like an ocean tide,” he says. COMAP operates by capturing blurry radio images of clusters of galaxies over cosmic time as opposed to sharp images of individual galaxies. This blurriness allows astronomers to efficiently capture all radio light coming from a larger pool of galaxies, including the faintest and dustiest galaxies never seen before. “We can find the average properties of typical, faint galaxies in this way without needing to know very precisely where any individual galaxy is located,” Cleary explains. “This is analogous to using a thermometer to determine the temperature of a large volume of water rather than analysing the motions of individual water molecules.” The Astrophysical Journal has published a summary of the new findings.

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Tsunamis are one of the most awe-inspiring and destructive natural disasters on Earth. These immense ocean waves, often triggered by undersea earthquakes or volcanic eruptions, can travel across entire ocean basins, wreaking havoc when they make landfall. Understanding how tsunami waves propagate across the deep sea is crucial not only for early warning systems but also for gaining insight into the Earth’s dynamic processes. Tsunamis are typically generated when a massive amount of energy is suddenly transferred to the ocean floor. This energy release can occur due to various geological processes, such as underwater earthquakes, volcanic eruptions, or even meteorite impacts. The primary driving force behind tsunamis is the vertical displacement of the seafloor, which displaces a significant volume of water and sets the tsunami in motion. Traveling Through Deep Water Once a tsunami is generated, it begins its journey through the deep sea, often traveling at speeds of up to 500-700 kilometers per hour (310-435 miles per hour) or even faster. Several key factors influence how tsunami waves behave in deep water: 1. Long Wavelength: Tsunami waves are characterized by their long wavelength, which can extend for hundreds of kilometers in deep water. This means that the distance between successive wave crests can be vast. However, their height in deep water is relatively small, typically less than a meter. 2. Minimal Surface Disturbance: In the open ocean, the sea surface remains relatively undisturbed by the tsunami wave passing beneath it. This is due to the large wavelength and small wave height, making tsunamis almost imperceptible to ships at sea. Here a video recording of a Tsunami in the high sea: 3. Energy Conservation: Unlike typical wind-generated waves, tsunamis conserve their energy as they travel across the deep ocean. This is because they are primarily driven by the movement of water particles below the surface, while wind-generated waves rely on the wind’s energy input. 4. Propagation Speed: Tsunami waves travel at remarkably high speeds due to their low wave height and vast wavelength. This rapid propagation allows tsunamis to cross entire ocean basins, even between continents, before slowing down as they approach shallower coastal regions. As tsunamis approach shallower coastal areas, their behavior undergoes significant changes. The wave’s energy, which was largely unnoticed in deep water, becomes compressed, causing the wave height to increase dramatically. The large increase in wave height and the rapid decrease in wavelength as they encounter shallower water lead to the well-known destructive effects of tsunamis when they reach the coastline.

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The concept of justice is central to any well-functioning society. Justice refers to the fair and ethical treatment of all members of society. It encompasses ideas like equality, human rights, and the rule of law. Historically, different societies have had different conceptions of justice based on their cultures, values, and forms of governance. In modern democracies, justice is often seen through the lens of democratic principles and processes. The close relationship between justice and democracy stems from some core overlap in their values – including equality, representation, participation, and human dignity. This article will examine how democracy can serve as an important means to achieving a just society. Democracy and Justice Democracy at its core promotes political equality – the idea that all citizens, regardless of background, should have equal rights, protections, and access to power. This directly ties in with principles of justice around equal treatment under the law. Democratic ideals reject systems where power and rights are determined by hereditary factors like nobility or gender. Instead, democratic power and rights are vested in the people. This popular sovereignty and political equality provide the foundation for pursuing a fair legal and political system. Beyond just equality, democracy’s focus on electoral representation helps create conditions for justice by giving groups agency in choosing leadership and setting policy. Competitive elections incentivize leaders to appeal to a broad base of constituents. This makes addressing unequal treatment of disadvantaged groups a relevant electoral issue. Representatives from diverse backgrounds also ensure marginalized groups have a voice in policy debates. Democracy’s response to disadvantaged groups contrasts with historical aristocracies, oligarchies, or monarchies where the privileged few had little incentive to consider justice for the marginalized. Additionally, democracy actively engages citizens in maintaining checks on potential government overreach. Democratic participation gives citizens nonviolent outlets to challenge unjust policies. Protests, referendums, recalls, and public advocacy are built into the democratic system, creating pressure valves for debate over justice. Authoritarian systems often violently suppress this kind of civic dissent and activism around injustice. Key Democratic Institutions and Practices for Justice Democratic societies employ certain governance structures and practices aimed at upholding rule of law and justice. While specific institutions vary, most modern democracies utilize a combination of separation of powers, checks and balances, an independent judiciary, and protections on civil liberties. Separation of powers between branches of government prevents unilateral action by dividing authority across executive, legislative, and judicial offices. This limits the possibility of an individual or small group dominating the state in a way that leads to unjust rule. Relatedly, institutional checks and balances like executive veto power, legislative confirmation votes, judicial review, and impeachment help different parts of the government stop overreaches of power by other parts. This constraint on government helps uphold justice by protecting against unfair policies or unequal treatment before the law. An independent judiciary free from political pressures or governmental interference is also essential for fair application of the law. Judges need autonomy to render judgments based on facts and legal principles rather than allegiance to the regime in power. Finally, democracies constitutionally enshrine civil liberties like free speech, assembly, and due process. These preserve space for citizens to vocalize injustice and demand redress through civic channels. Competitive elections are the most high-profile democratic practice impacting justice. The need to win elections incentivizes politicians to listen and respond to citizen concerns over fairness and equality. Representatives and parties that promote justice and inclusion are rewarded at the ballot box, while those seen as unjust risk electoral defeat. For example, in the 1960s and 70s, US politicians passed major civil rights laws and programs in response to activist pressure and changing public opinion around racial justice. The threat of losing office pushed action on issues of injustice historically neglected. Competitive elections help translate public priorities about justice into official policy. In a similar fashion, universal suffrage and political participation give citizens leverage and voice to demand fairer treatment. Excluded groups often bear the brunt of injustice given their lack of representation. Broad electoral participation changes this dynamic by allowing disadvantaged populations to vote and actively shape politics. Democratic participation provides a counterweight to the influence of elite economic and political interests who may oppose reforms to the unjust status quo. Extensive participation makes promoting justice a political necessity, not just ideal. For example, expanding the vote to women and minorities in the US led to new policies and legal protections addressing their specific justice concerns. Majority rule via elections is a democratic principle whereby leaders and policies are chosen based on popular consent, not despotic dictate. This idea aligns with justice by giving the broader public power to enact laws in their collective interest, blocking unjust policies that only benefit the few. While majority rule risks trampling minority rights, democracies build in constitutional safeguards to uphold legal equality and protect minority voices. Concepts like ‘tyranny of the majority’ emerged precisely to highlight how democratic majorities must balance their power with minority protections to ensure justice. Several key democratic practices aim at facilitating informed, responsive, and ethical governance. Government transparency through free flow of information empowers journalists and citizens to expose injustice. Robust public debate allows truth and justice to triumph over misinformation and prejudice. Democratic norms on rule of law, anti-corruption, and public service instill just governance. Oversight procedures like legislative hearings, independent audits, and public comment periods create accountability and feedback mechanisms to catch and remedy injustice. An engaged civil society of citizens, civic groups, and social movements provides bottom-up pressure on the system to uphold justice. Challenges and Limits While democracy provides tools to pursue justice, it has real limitations and challenges. Unjust policies and treatment have emerged even in mature democratic systems. Democracy’s reliance on electoral majorities means that minority groups still risk having their rights and interests neglected orsteamrolled. Constitutional protections on rights and separation of powers aim to mitigate this but don’t completely solve it. Persistent issues like prisoner disenfranchisement, police brutality, anti-immigrant sentiment demonstrate holes in the system. Similarly, democracy’s commitment to free speech and pluralism means it allows space for hateful, unjust views. Democratic values prevent outright bans of racist or nationalist ideologies, for example, so these unjust forces still exert influence. This forces disadvantaged groups to constantly fight for justice and inclusion against vile opponents. The democratic principle of popular sovereignty does confer ultimate power to ‘the people.’ However, influence in democracies still tilts heavily toward societal elites even if formal rights are equal. Wealth gives some citizens outsized influence on elections and policy through campaign finance, lobbying, think tanks, and other channels. These means can distort policymaking in ways that undermine justice and equality. Finally, democracies remain vulnerable to populist surges that can weaken protections for minority rights and constitutional constraints on power. Populist leaders centralize authority and inflame majoritarian impulses in ways that risk trampling principles of impartial justice. Recent democratic backsliding in places like Hungary and Turkey illustrate this danger if democratic norms and institutions erode. While imperfect, democracy remains humanity’s greatest institutional hope for achieving justice in actual governance. But continued progress is not automatic. Maintaining justice in democratic societies requires eternal vigilance by engaged citizens and leadership animating our better angels. It demands doubling down on inclusion, reforming systems skewed toward the powerful, and upholding norms of fair play and equal treatment. Fulfilling democracy’s promise on justice also means learning from peers around the world experimenting with novel democratic reforms. A system built around popular power must continue striving to redeem the abuses of that power and direct it toward the cause of justice. Justice and democracy share a profound connection. Democracy’s foundational principles – political equality, inclusive representation, majority rule, participation, and civil liberties – provide mechanisms to pursue fair and ethical treatment for all. Key democratic institutions – like separated powers, competitive elections, and protections for minority rights – aim to enshrine justice against threats of despotism or mob rule. However, democracies still struggle to fully deliver justice, particularly for disadvantaged groups. Discrimination, corruption, and demagoguery continue to test democracy’s capacities for justice. But at its best, democracy channels society’s diverse voices into a self-correcting system willing to confront injustice. The journey toward justice is winding and incomplete. But by adhering to its core values and reforming institutions, democracy provides hope for travelers on that road. Dahl, Robert A. On Democracy. Yale University Press, 2000. Lipset, Seymour M. “Some Social Requisites of Democracy: Economic Development and Political Legitimacy.” American Political Science Review, vol. 53, no. 1, 1959, pp. 69-105. Carey, John M. “Does It Matter How a Constitution is Created?” Lessons from Democratic Constitutional Design, edited by Tom Ginsburg and Rosalind Dixon, Cambridge University Press, 2022, pp. 167-200. Vile, John R. Essential Supreme Court Decisions: Summaries of Leading Cases in U.S. Constitutional Law. Rowman & Littlefield, 2018. Mayhew, David R. Congress: The Electoral Connection. Yale University Press, 2004. Keyssar, Alexander. The Right to Vote: The Contested History of Democracy in the United States. Basic Books, 2009. Powell, G. Bingham. “Constitutional Design and Citizen Electoral Control.” Journal of Theoretical Politics, vol. 1, no. 2, 1989, pp. 107-130. Norris, Pippa. Why Electoral Integrity Matters. Cambridge University Press, 2014. Guinier, Lani. The Tyranny of the Majority: Fundamental Fairness in Representative Democracy. The Free Press, 1994. Sunstein, Cass R. #Republic: Divided Democracy in the Age of Social Media. Princeton University Press, 2017. Gilens, Martin, and Benjamin I. Page. “Testing Theories of American Politics: Elites, Interest Groups, and Average Citizens.” Perspectives on Politics, vol. 12, no. 3, 2014, pp. 564-581. Levitsky, Steven, and Daniel Ziblatt. How Democracies Die. Crown, 2018.

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Many students of math find word problems challenging, but it doesn’t have to be that way. This three-step process makes math problems easier! Better yet, it helps students train their skills in ways that are more easily applied to life beyond school, too. When solving a word problem, a student should always follow these three steps: - Read the entire problem without trying to solve it yet - Determine which part of the problem is asking for an actual answer - Only then do they use the information from the problem to get the appropriate answer This process is applicable across all types of math, and helps students practice their problem-solving skills in a way that can be applied to their lives beyond the classroom. Each step has a key reason for why it is done this way, and understanding the reasons can help kids accelerate their learning as well. - By reading the problem in full without trying to solve it first, students solve one of the most common errors that they can make for word problems – making a hasty answer that uses the right numbers and a wrong understanding. A full reading of the problem means that students have the full context of whatever situation the problem describes before they start diving into equations. For most students, this method even ends up being faster, because they aren’t distracted by trying to assemble possible solutions and trying to read the problem at the same time! - Once students have a grasp of the general situation and context of a problem, it’s important to identify what actual result is needed. Many word problems discuss several different aspects of a situation, often with multiple people and steps, but only need one specific answer. By determining what sort of answer is needed first, students avoid getting lost in unnecessary equations and confusing themselves. - Finally, now that a student knows what information the problem gives them and what answer they need to aim for – they can solve it! As students get more comfortable with word problems, step 2 becomes something they’ll pick up in the course of reading a problem, making the process even faster. Here’s an example problem that students can use to try this process. This particular example is appropriate for second to fourth grade students depending on their skills. Jenny has a box full of quarters which she sorts into piles. If she has $12 of quarters, and sorts them into six equal piles, how many quarters does it take to make two of the piles? Reading this through gives us some very important information: This problem is all about quarters, even though the number of quarters is provided to us in dollars. There’s no need to start working with the numbers until a student also figures out what sort of answer the problem needs. The problem mentions that the quarters get separated into six piles, and wants to know how many quarters it takes to make two of those six piles. Now a student can make a plan: First, to convert twelve dollars into a number of quarters. Then, divide that number of quarters into six groups. Finally, add two of the groups together or double them. (Older students, or especially clever ones, may have already caught that they could just divide the number of quarters into three groups. That works too!) Twelve dollars thus becomes forty-eight quarters; forty-eight quarters get split into six groups of eight quarters each; and two of those groups together make up sixteen quarters. And thus the answer is sixteen quarters. Interested in learning more? Have a student who wants to improve themselves? We run summer camps, holiday camps, and weekly classes all year long for ages 6 through 14 and grades 2 through 8 to improve all these skills and more – and to have fun doing it. You can see our offerings here and choose which classes are right for your student!

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The structure of DNA will ultimately be revealed as the history section ends. Chargaff’s rules for base pairing and the x-ray diffraction photograph reinforces understanding of this molecule’s structure. Constructing a DNA molecule will demonstrate its basic structure as well as provide a model for future discussion of DNA function. It is worthy to note that there are several forms of DNA: B-DNA and Z-DNA are the two most important. Z-DNA is far less common than B-DNA. B-DNA is the double helix structure proposed by Watson and Crick and is the form DNA usually has in solution. This unit will focus only on the B form of DNA. DNA, the hereditary material passed on from cell to cell, is a nucleic acid. A nucleic acid is a macromolecule that is composed of repeating nucleotides. There are two kinds of nucleic acids, DNA is one kind, RNA is the other. A DNA molecule consists of a very long chain of repeating units. The repeating units are called nucleotides. A nucleotide has three components: a 5-carbon sugar (deoxyribose for DNA or ribose for RNA), a phosphate group (PO4) and a nitrogenous base (either a purine or a pyrimidine, which refer to the structure of the nitrogenous base- either two rings or one respectively). In a DNA molecule the four nitrogenous bases are adenine, thymine, guanine, and cytosine with the purines being adenine and guanine and the pyrimidines being thymine and cytosine. Adenine (purine) always bonds to thymine (pyrimidine) and guanine (purine) always bonds to cytosine (pyrimidine). [NOTE: to remember which is a purine and which is a pyrimidine- just recall that pyrimidine has a “Y” in its name and so do the two pyrimidine bases, thYmine and cYtosine] In an RNA molecule, thymine is not found, but the nitrogenous base uracil (a pyrimidine) is found and bonds with adenine during transcription. The shape of a DNA molecule is like a ladder, twisted or coiled into a double helix. The rungs of our ladder would be the nitrogenous bases bonded to each other. The base pair adenine/thymine are held together as a rung of this ladder by two hydrogen bonds; the base pair guanine/cytosine are held together by three hydrogen bonds. The nitrogenous base pairs are bonded to a sugar phosphate backbone- a chain of alternating sugar and phosphate groups. A nitrogen from the nitrogenous base forms a covalent bond with the first carbon in a sugar molecule. The fifth carbon in the sugar molecule bonds with an oxygen from a phosphate ion. This same phosphate ion uses another oxygen to bond to the third carbon in another sugar molecule, and this repeated chain forms the backbone of a DNA strand. (See diagram #1 below.) But since DNA is double stranded, there are two sugar phosphate backbones. It is estimated that there are at least 3 billion base pairs on a human DNA molecule. Diagram #1. A diagram of the sugar phosphate backbone of a DNA molecule. This diagram shows the linkage between a phosphate group and the deoxyribose sugar.

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Introduction to the Simplest if Statement in Python=== Python is a popular programming language that is widely used in various industries. One of the most fundamental concepts in Python development is the if statement. The if statement is a conditional statement that allows a programmer to execute certain blocks of code depending on whether a certain condition is true or false. In this article, we will explore the simplest if statement in Python, its syntax, implementation, common errors, and best practices that every Python developer should consider. Basic Syntax and Implementation of if Statement in Python The basic syntax of an if statement in Python is "if condition:". The condition should be a Boolean expression that evaluates to either True or False. The colon (:) indicates the beginning of a new block of code that will be executed if the condition is True. This block of code is indented to indicate that it belongs to the if statement. Here's an example: x = 5 if x > 3: print("x is greater than 3") In this example, the condition is "x > 3", which evaluates to True since x is 5. Therefore, the code inside the if statement (i.e., print("x is greater than 3")) is executed, and the output is "x is greater than 3". Common Errors and Best Practices to Consider in if Statement Development One common error that can occur when using if statements in Python is forgetting to indent the code inside the if statement. This can lead to a syntax error because Python requires indentation to indicate the beginning and end of a block of code. Another common error is using the assignment operator (=) instead of the comparison operator (==) in the condition. This can lead to unexpected results because the assignment operator will always return True. To avoid these errors, it is best to follow the best practices when developing if statements in Python. One best practice is to use descriptive variable names in the condition. This makes the code more readable and easier to understand. Another best practice is to use parentheses around complex conditions to make the code more readable. For example: if (x > 3) and (y < 10): print("x is greater than 3 and y is less than 10") This code is easier to read than if x > 3 and y < 10 because the parentheses make it clear which conditions are being evaluated together. It is also recommended to use comments to explain the purpose of the if statement and any assumptions made in the condition. This makes the code easier to maintain and update in the future. The if statement is a fundamental concept in Python development, and every Python developer should understand its syntax, implementation, common errors, and best practices. By following the best practices, you can write clean, readable, and maintainable code that is easy to understand and modify. Remember to always test your code thoroughly to ensure that it works as expected. With these tips in mind, you can confidently use if statements in your Python projects.

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One measure of central tendency in statistics. The term average is popularly used to refer to a value that is typical of a group. For example, a person may be described as being of average height or average intelligence. Educators and school administrators may describe the average for the population of students in their school. Average always describes a relative value; for example, the average score on a standardized test for students in a particular class may or may not equal the average score for all students in the school. Yet another value will be the average for all test-takers nationwide. Thus, the average is often used as a way to compare attributes of two different groups. Average is one of the measures of central tendency used in statistics. There are three precise measures of central tendency calculated by statisticians when studying sets of data. The mean is calculated by adding together all the numbers in the set being studied, and dividing the total by the number of data points. For example, if the statistician is calculating the mean test score for a group of 27 test-takers, he would add together the scores of all 27 people, and divide the total by 27. Grade-point average, calculated by adding all the numerical values for a student's grades together and dividing by the number of grades received, is an example of a mean. The median, or midpoint, for the set of test scores would be the score precisely at the midpoint when the scores are ranked in numerical order. The mode is the score that was achieved most often.

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Equilibrant forces are those that act on a body at rest and counteract the force pushing or pulling the body in the opposite direction. Equilibrant forces establish equilibrium for an object and make the object motionless. Equilibrant forces act on virtually every object in the world that is not moving.Know More The force of gravity is pulling down a cup sitting on a desk. The only way the cup can keep from crashing into the ground is if something pushes up on it at least as hard as gravity is pulling it down. The table or counter top holding up the cup supplies the equilibrant force, which keeps the cup up. If the table exerted more than equilibrant force on the cup, the cup would rise in the air. Equilibrant forces can push or pull on an object as long as both forces are imparting the same type of force, but in the opposite direction. Sometimes, equilibrant forces work in concert with each other to offset opposing forces. For example, if three cables suspend a load, each is imparting a force that is equal to one-third of the force of gravity. Likewise, a load suspended by four cables imparts one-fourth of the pull of gravity on each cable.Learn More The equation for determining the net force acting on an object is F = ma, or force equals mass times acceleration. Net force is measured in terms of acceleration, which means a change in velocity. If there is no change in velocity, the net force is considered to be zero.Full Answer > A net force is the remaining force that produces any acceleration of an object when all opposing forces have been canceled out. Opposing forces decrease the effect of acceleration, lowering the net force of acceleration acting on an object.Full Answer > Friction always opposes motion between two surfaces, although it is not a fundamental force of the universe like gravity. The coefficient of friction is used to describe the ratio of friction between two bodies and the outside force pressing them together.Full Answer > When a force is applied to an object resting on a surface, a retarding force is that which opposes the force being applied to the object. A retarding force is usually that of friction, which must be overcome when moving an object resting on a surface. If the object is being moved upward along an inclined plane, gravity represents an additional force that must be overcome.Full Answer >

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Children's LiteratureChildren today press buttons and things happen: televisions change channels, microwave ovens cook food, and cell phones activate. Computers and machines follow instructions to do these things and much more. But people must write the instructions, or programs, for machines to follow. Children will get a sense of how successful programs are written with this primer. Using clever illustrations, photographs, and age-appropriate text, readers should see the correlation between sound instructions and the desired result in technology. This book provides basic instructions for readers to create computer programs for simple activities, such as drawing shapes and patterns on the computer. Testing and re-testing programs to eliminate mistakes is emphasized. Excellent illustrations demonstrate that designing a control sequence involves careful planning. To program a set of traffic lights, for instance, programmers must ask and answer many questions before writing instructions. Readers are urged to draw a story board before undertaking a complicated control sequence. This title, part of the "Learn Computing" series, does a great job of showing children the thought processes and work that go into writing computer programs. An index and glossary are found at the back of the book. 2004, QEB Publishing, Ages 9 to 12. Jeanne K. Pettenati, J.D.

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Activity sheet with a large world map in the centre. Labels for the continents and oceans at the top and bottom, students can cut and stick or link up with lines. They're then asked to find their home country and label it to understand where it is in the world. Great to photocopy onto A3 to increase the map size. 1. PowerPoint Lesson - explaining when to use 'ge' or 'dge' at the end of works ending in the phoneme /j/. 26 slides in total. (The /dʒ/ sound spelt as ge and dge at the end of words National curriculum , English programmes of study Year 2) This resource includes a fully editable, interactive and highly visual powerpoint lesson explaining when to use 'ge' or 'dge' at the end of words. Content of powerpoint includes - Rules for adding 'dge' and 'ge' (long and short vowel sounds, 'ge' after letters 'r' and 'n' as in large and fridge) - Opportunities to practise spellings - Individual / paired / group timed activity - finding as many' dge' and 'ge' words as possible in 5 minutes) 2. A set of 15 differentiated worksheets on words ending in 'ge' or 'dge' at the end of words. (The /dʒ/ sound spelt as ge and dge at the end of words National curriculum , English programmes of study Year 2) Content and tasks include: 1. Missing words worksheets. (2 differentiated) 2. Anagrams - (3 differentiated) 3. Sets of spellings - 4 worksheets 4. Using ge / dge words in sentences (2 differentiated worksheets) 5. Word searches (3 differentiated) 6. Sorting words into ge / dge / vower 'r' / vowel 'n' categories (1 worksheet) Appropriate for Year 2 pupils and older SEN students who have yet to master the basics in phonics.

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Electric Current is defined as the amount of electric charge flowing through any cross section of conductor in unit time. It is denoted by I and its SI unit is Ampere (A). Voltage is also known as Electric Potential Difference Or Electric Potential. Consider a positively charged sphere. This sphere would have an electric field around it,in which it will exert attractive force for a negative charge and repulsive force for a positive charge. Now, consider a positively charged particle just outside the electric field of the sphere. We call this position as infinity. Now, we would have to exert force and do work on the particle to bring it near to the sphere against the force of repulsion. Suppose we bring it to a point A in the electric field and leave the particle. Now, the work done by us gets stored in the particle in the form of Electric Potential Energy. As soon as we leave the particle, this potential energy changes into kinetic energy and the particle moves away from the sphere (due to repulsive force). Now consider that we bring the same particle from point A mentioned above to point B further closer to the sphere against the force of repulsion. This particle would now gain more electric potential. The difference in electric potential at point A and Point B is called Electric Potential Difference between these two points or simply Voltage (V). Thus, Electric Potential Difference (Voltage) can be defined as the work done to bring a unit positive charge from Point A to B against the electric force of repulsion in the electric field.

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Fifteenth Amendment, Guaranteeing Right to Vote, is Ratified The Fifteenth Amendment was the last of three amendments introduced in the wake of the Civil War (often referred to as the Reconstruction Amendments). The Thirteenth Amendment abolished slavery. The Fourteenth Amendment declared that “all persons born or naturalized in the United States . . . are citizens of the United States and of the State wherein they reside.” The Fifteenth Amendment, ratified on this day, granted African-American men the right to vote by declaring that the “right of citizens of the United States to vote shall not be denied or abridged by the United States or by any state on account of race, color, or previous condition of servitude.” However, through the use of poll taxes, literacy tests and sheer intimidation and terrorist tactics, Southern states were able to effectively disenfranchise African-Americans. It would take the passage of the Voting Rights Act of 1965, signed by President Lyndon Johnson on August 6, 1965, before the majority of African-Americans in the South were registered to vote. Read the Fifteenth Amendment: http://www.archives.gov/exhibits/charters/constitution_amendments_11-27.html Learn about the history of the right to vote: Alexander Keyssar, The Right to Vote: the Contested History of Democracy in the United States (2000)

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Proving and solving of inequalities Proving of inequalities. Basic methods. Solving of inequalities. Equivalent inequalities. Method of intervals. Double inequality. Systems of simultaneous inequalities. Proving of inequalities. There are some ways to prove inequalities. Well consider them to prove the inequality: where a a positive number . 1). Using of the known or before proved inequality. It is known, that: ( a 1 )² 0 . Opening the brackets, well receive: Hence it follows: which was to be proved. 2). Estimating of the sign of difference between sides of inequality. Consider the difference between the left and the right sides: moreover, the equality takes place only if a = 1 . 3). Reductio ad absurdum proof ( an indirect proof ) . Assume the contrary proposition: Multiplying both of the sides by a , well receive: a² + 1 < 2a, i.e. a² + 1 2a < 0 , or ( a 1 ) ² < 0, that is wrong. ( Why ? ) . The received contradiction proves the validity of the considered inequality. 4). Using of an indefinite inequality. An indefinite inequality is an inequality with the sign \/ or /\ , when we dont know how to turn this sign to receive the valid inequality. There are the same rules of operations as for inequalities, containing the signs > or < .Consider the indefinite inequality: Multiplying both of the sides by a, we receive: a²+ 1\/ 2a, i.e. a² + 1 2a \/ 0 , or ( a 1 )²\/ 0 , but here we know, how to turn the sign \/ to receive the valid inequality. ( How ? ). Turning it in the whole chain of transformations to the right direction, we receive the inequality, which was to be proved. Solving of inequalities. Two inequalities, containing the same unknowns, are called equivalent, if they are valid at the same values of the unknowns. The same definition is used for the equivalence of two systems of simultaneous inequalities. Solving of inequalities is a process of transition from one inequality to another, equivalent inequality. For this purpose main properties of inequalities are used (see above). Besides this, an exchange of any expression by another, identical one may be used. Inequalities can be algebraic (containing only polynomials) and transcendental (for instance, logarithmic or trigonometric inequalities). Well consider here one very important method, often used at solving algebraic inequalities. Method of intervals. Solve the inequality: ( x 3 )( x 5 ) < 2( x 3 ) . Its impossible to divide both of the sides of this inequality by ( x 3 ), because we dont know the sign of this binomial (it contains unknown x ). So, we must transfer all terms to the left-hand side:( x 3 )( x 5 ) 2( x 3 ) < 0 , and after factoring the left-hand side expression is following:( x 3 )( x 5 2 ) < 0 , we receive: ( x 3 )( x 7 ) < 0. Now we determine the sign of the left side product in different numerical intervals. Note, that x = 3 and x = 7 are the roots of this expression. Therefore, the whole numerical line is divided by these roots to the following three intervals: In the interval I ( x < 3 ) both factors are negative, so their product is positive; in the interval II ( 3 < x < 7 ) the first factor ( x 3 ) is positive, and the second factor ( x 7 ) is negative, so their product is negative; in the interval III ( x > 7 ) both of the factors are positive, so their product is also positive. Now we must select the interval within which our product is negative. This is the interval II , hence we have the solution: 3 < x < 7. The last expression is the so called a double inequality. It means that x must be greater than 3 and less than 7 simultaneously. E x a m p l e . Solve the following inequality by the method of intervals:( x 1 )( x 2 )( x 3 ) ( x 100 ) > 0 . S o l u t i o n . The roots of the left-hand side of this inequality are: 1, 2, 3, The numerical line will be divided by these roots into 101 intervals: Note, that number of the factors from the left is equal to 100, i.e. an even number. Hence, at x < 1 all factors are negative and theirproduct is positive. Then well have a change of the product sign at transition of any next root. Therefore, the next interval, within which the product is positive will be ( 2, 3 ) , then ( 4, 5 ) , then ( 6, 7 ) , , ( 98, 99 ) and the last interval is x >100. So, the given inequality has the solution: x < 1, 2 < x < 3, 4 < x < 5 , , x >100. Thus, to solve some algebraic inequality its necessary to transfer all terms to the left (or to the right) side of the inequality and to solve the corresponding equation. After this, the numerical line is divided by the found roots into some intervals. In the last stage of solution it is necessary to determine the sign of the polynomial within each of these intervals and to select the necessary intervals according to the sense of your inequality. Note that the most of transcendental inequalities are reduced by exchange of unknown to an algebraic inequality. Then it should be solved in new unknowns; after the inverse exchange of unknown it is solved finally in the given unknowns. Systems of simultaneous inequalities. To solve the system of simultaneous inequalities it is necessary to solve each of them and to compare their solutions. This comparison results to one of two possible cases: either the system has a solution as a whole or does not. E x a m p l e 1. Solve the system of simultaneous inequalities: S o l u t i o n. The first inequality solution: x < 4 ; and the second: x > 6. Thus, this system of simultaneous inequalities has no solution. ( Why ? ) E x a m p l e 2. Solve the system of simultaneous inequalities: S o l u t i o n. The first inequality as before gives: x < 4; but the second inequality gives in this case: x > 1. Thus, there is the solution: 1 < x < 4.

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By Crystal R. Stanley on August 10 2018 23:10:23 In KS2 children are taught that decimals are another way of writing fractions. The hundred number square is a really good way of showing children the equivalence between fractions and decimals. Long Division. There are different methods for dividing multi-digit numbers (long division). One way is a combination of estimation/ trial and error and multiplication. There is also a commonly used algorithmic method that is well explained and illustrated here at mathisfun.com. It all starts here with addition! Learning addition is the first step on your way to subtraction, and makes up the foundation of all of the strategies used to teach multiplication. These math fact timed tests and multiple digit addition problems should make up the core of your strategies for teaching addition concepts, but when you are ready for alternative strategies: - Picture Math Addition. - Addition Flash Cards. - Addition and Subtraction Grid Puzzle Worksheets. The addition worksheets on this page introduce addition math facts, multiple digit addition without regrouping, regrouping, decimals and other concepts designed to foster a mastery of all things addition. All of the worksheets include answer keys, and there are four versions of each worksheet with different problems.

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The holidays of Emancipation Day and Juneteenth are occasions for learning about the U.S. history of slavery, abolitionism, and emancipation. In order to learn the meaning and significance of “Emancipation” and “Juneteenth,” readers first learn about “a terrible part of America’s history called slavery” and the brave heroes and heroines who fought to end it. A section called “How Did Slavery Begin in America?” explains how traders brought captured Africans across the ocean in chains, then sold them in markets to white owners, who became dependent on slave labor. This section points out that the rights and equality established in the Declaration of Independence did not include the enslaved population. Next, sections on Frederick Douglass, Sojourner Truth, and Harriet Tubman describe the hard work that such abolitionists undertook. A section on the Civil War includes the Compensated Emancipation Act and the military operation Harriet Tubman led to help the Union Army rescue slaves. This section includes mention of the “Black Codes” that limited African-Americans’ freedom for many more years. The final few pages detail the history of the District of Columbia Emancipation Day holiday and the origin and traditions of the Juneteenth celebrations in Texas and elsewhere. Vivid modern photographs and historical illustrations cover half of every spread. Packed with information but more engaging than a textbook, this volume, like others in the series (Let’s Celebrate Women’s Equality Day publishes simultaneously), uses an honest yet positive approach to presenting the fight against injustice in U.S. society. A solid option for introducing the historical context of the holidays. (Nonfiction. 7-11)

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In developing number concepts and number sense children learn to recognize numbers as odd or even. Two books that are helpful are Even Steven and Odd Todd by Kathryn Cristaldi and Bears Odd, Bears Even by Harriet Ziefert. Opportunities to develop an understanding of odd and even numbers are bountiful throughout the school day. 1. While counting any found objects or manipulatives have the students group the items in pairs. Emphasize that an item that does not have a partner, or any ‘left over’ item is odd. 2. Have students skip-count by 2’s. 3. Give students a hundred’s chart and two crayons. Have them shade the even numbers with one color and the odd numbers with a different color.

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This tutorial will take you through writing conditional statements in the Python programming language. If statement We will start with the if statement, which will evaluate whether a statement is true or false, and run code only in the case that the statement is true. An ifelse statement executes one set of statements when the condition is true and a different set of statements when the condition is false. In this way, a ifelse statement allows us to follow two courses of action. Simple Conditions. The statements introduced in this chapter will involve tests or conditions. More syntax for conditions will be introduced later, but for now consider simple arithmetic comparisons that directly translate from math into Python. In the heart of programming logic, we have the if statement in Python. The if statement is a conditional that, when it is satisfied, activates some part of code. The if statement is a conditional that, when it is satisfied, activates some part of code. An important part of coding in Python is learning to express conditional logic. Python has a class designated specifically for this called Boolean. In this tutorial, well cover the basics of the Boolean class and show you what role it plays in developing important coding tools, such as if, else, and elif statements. Statements are the smallest, This reference manual describes the syntax and core semantics of the language. It is terse, but attempts to be exact and complete. The semantics of nonessential builtin object types and of the builtin functions and modules are described in The Python Standard Library. Automate the Boring Stuff with Python Programming; If statements. Consider this application, it executes either the first or second code depending on the value of x. I am new to python and just learning the syntax. (I am experienced in other languages). What is the syntax if I want more than one line of code between if: and else:and Python if elif else: Python if statement is same as it is with other programming languages. It executes a set of statements conditionally, based on the value of a logical expression. Also read if else, if elif else. The elif statement allows you to check multiple expressions for TRUE and execute a block of code as soon as one of the conditions evaluates to TRUE. # ! usrbinpython var 100 if var 200: print" 1 Got a true expression value" print var elif var 150: print" 2 Got a true expression value Python if Statement Syntax if test expression: statement(s) Here, the program evaluates the test expression and will execute statement(s) only if the text expression is True. If the text expression is False, the statement(s) is not executed. Python if statements are very commonly used to handle conditions. If you learn data coding, here's an article to learn the concept and the syntax!

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A simple motor works on the basis of torques on current loops. We will apply the fundamental rules of magnetic fields and current loops to understand how a simple electric motor works. We saw that a segment of a current-carrying wire feels a force from a magnetic field. Here, the current is to the right, the B field is into the page and the force is upward. Here we have a current loop immersed in a magnetic field. The forces cancel on this current loop because the magnetic field is perpendicular to the plane of the loop. Here, the plane of our current loop is no longer perpendicular to the magnetic field. The forces on the sides of the loop always cancel. Torque on the upper segment pulls upward while torque on the lower segment pulls downward, tending to rotate the loop in the magnetic field. We have defined the moment arm d in terms of the current segment l. Recalling that μ = IA, this allows us to write the torque as the cross product of the magnetic moment and the ambient magnetic field. This sequence of diagrams illustrates how a simple motor works. The magnetic field exerts a force on a current loop, at right angles to the direction of the field and to the direction of the current. This torques the loop and causes it to rotate. As the current loop turns, the magnetic field continues to exert a force on it. When the loop turns far enough, the force would work to stop turning it, In a motor, the polarity of the current is switched to run the other way. This makes the force on the loop such that it continues to turn. This is the basic mechanism of an electric motor. Check out this website for a cool animation of a simple motor. Find more detail on how a motor works here.

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First, we will concentrate on punctuation. Discuss capital letters and full stops. Do they know any other kinds of punctuation? Where does the punctuation need to go? Work through the sentences and paragraph in the pdf below to add the capital letters and full stops in the right places. Re-read Tiddalik and think about the structure of the story and language used. Discuss what happens at the beginning, middle and end of the story.Draw a story map for the story of Tiddalik. Then add character names and labels/wow words to the story map. Use the story map from yesterday to retell the story. Write the story of Tiddalik. Think very carefully about punctuation (capital letters and full stops), adjectives and wow words to make it sound exciting and using words to extend sentences (and, but, because). Remind children about nouns, adjectives and verbs. Look at the story of Tiddalik and find the different types of words. Fill in the table on the pdf below. Then try to use some of the words in sentences. Can you put a noun, adjective and verb all in one sentence? Recap on the singular and plural work from last week. Look through the power point as a reminder. On the pdf below, make the singular words into plurals. Then use them in sentences. Remember to use punctuation.

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This article explains some of those relationships. I was asked, I need an easy and helpful way to teach writing equations. But word problems do not have to be the worst part of a math class. By setting up a system and following it, you can be successful with word problems. So what should you do? Here are some recommended steps: Read the problem carefully and figure out what it is asking you to find. Usually, but not always, you can find this information at the end of the problem. Assign a variable to the quantity you are trying to find. Most people choose to use x, but feel free to use any variable you like. For example, if you are being asked to find a number, some students like to use the variable n. It is your choice. Write down what the variable represents. At the time you decide what the variable will represent, you may think there is no need to write that down in words. However, by the time you read the problem several more times and solve the equation, it is easy to forget where you started. Re-read the problem and write an equation for the quantities given in the problem. This is where most students feel they have the most trouble. The only way to truly master this step is through lots of practice. Be prepared to do a lot of problems. The examples done in this lesson will be linear equations. Solutions will be shown, but may not be as detailed as you would like. If you need to see additional examples of linear equations worked out completely, click here. Just because you found an answer to your equation does not necessarily mean you are finished with the problem. Many times you will need to take the answer you get from the equation and use it in some other way to answer the question originally given in the problem. Your answer should not only make sense logically, but it should also make the equation true. If you are asked how fast a person is running and give an answer of miles per hour, again you should be worried that there is an error. If you substitute these unreasonable answers into the equation you used in step 4 and it makes the equation true, then you should re-think the validity of your equation. When 6 is added to four times a number, the result is What are we trying to find? Assign a variable for the number. We are told 6 is added to 4 times a number. Since n represents the number, four times the number would be 4n. If 6 is added to that, we get. We know that answer is 50, so now we have an equation Step 5: Answer the question in the problem The problem asks us to find a number. The number we are looking for is The answer makes sense and checks in our equation from Step 4. The sum of a number and 9 is multiplied by -2 and the answer is We are then told to multiply that by -2, so we have.equations in text Technical writing often contains equations, however the use of equations is not commonly discussed in books on style and composition. She shoots, she scores! Shoot hoops with Penelope by solving math equations in this basketball multiple choice game. Kids help Penelope move around the court to make baskets by answering a combination of multiplication, division, addition, and subtraction problems. Buzzmath is currently not available for your mobile device. Visit our support page to see which devices we support. Have any questions? We're here to help! Contact us anytime. Learn about equations and inequalities that have variables in them. These tutorials focus on solving equations and understanding solutions to inequalities. Free Pre-Algebra worksheets created with Infinite Pre-Algebra. Printable in convenient PDF format. Equations help a bunch here. Guided Lesson Explanation - I tried everything to keep it to one page, but it didn't work out. Practice Worksheet - The word problems are super random.

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Chapter 14.1 Feudalism and the Manor System In Europe (c.500 – 1500) • Objectives: • Learn when the Middle Ages were and what they were like • Find out how land and power were divided under feudalism. • Learn how the manor system worked. • Discover what life was like for peasants and serfs. When were the Middle Ages? The Fall of Rome marked the end of the ancient world and the beginning of a new era. The new time period is known as the Middle Ages, or the Medieval Period or the Dark Ages. This period lasted until about 1450. Knight A man who received honor and land in exchange for serving a lord as a soldier. He was expected to be loyal to the lord who knighted him. Charlemagne- the king of the Franks (put under name) The Franks invaded Gaul. He expanded his kingdom by conquering smaller ones. He ruled for nearly 50 years and spread the Christian religion. After his death, his empire was divided among his sons who fought against each other. Why did Charlemagne's empire fall apart? • He divided his empire into three parts for each of his sons. • His sons fought one another, which weakened the empire. • See their names- • Charles, Louis, and Lothair (lots of hair) • Vikings attacked the weakened empire. Feudalism A system where land was owned by kings but held by lords and vassals in return for their loyalty. Lords Lords Fief A fief is a grantof something of value, most often land, from a king to his lord or to his vassal. Vassal • A vassal could be a lord. • They were expected to raise armies then lead the armies that would fight for their land. • They also paid taxes (in the form of crops) to their lords. What did lords give vassals in exchange for the vassals’ loyalty? • Lords provided their vassals with land. • The lords also asked for their advice before making laws or going to war. Manor A manor is a large estate that included farm fields, pastures, and often an entire village. Lord of the Manor Usually a vassal of a king or a more powerful lord. Their duties included: • They ruled the people on his manor • They made rules and acted as a judge • They chose someone to oversee the farming and other daily work • They collected taxes from peasants She is the lady of the manor. Her duties included: Noblewomen • She managed the household • She supervised servants • She performed any necessary medical tasks • She also acted as the “lord of the manor” when the lord was gone. Peasants This group made up the majority of people during the Middle Ages. They made their living as farmers and laborers. Serfs Serfs are peasants who were considered to be part of the manor. Peasant Life Peasants were responsible for: • raising food for the lord • and raising food for their family What was life like for medieval peasants? Peasants had a hard life because: • All men, women, and children were required to work • They gave most of their harvest to their lord • They lived in cramped one-room huts • They slept on cloth sacks stuffed with straw

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Before the lesson Download classroom resources - To understand how computers have changed and the impact this has had on the modern world Pupils should be taught to: - Understand computer networks, including the internet; how they can provide multiple services, such as the World Wide Web, and the opportunities they offer for communication and collaboration - Use search technologies effectively, appreciate how results are selected and ranked, and be discerning in evaluating digital content - Select, use and combine a variety of software (including internet services) on a range of digital devices to design and create a range of programs, systems and content that accomplish given goals, including collecting, analysing, evaluating and presenting data and information For pupils needing extra support: Suggest a Google Doc and select only a handful of the computers from the list written in date order with one fact about each. Pupils working at greater depth: Encourage them to express their findings using whatever medium they prefer. Make sure they include a picture and some information about why each computer type was built.

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Lesson One What do we know about the type of rock exposed at the site? Introduction to the site to be used or visit to the Virtual Quarry Resource Students should use Ordnance Survey and Geological Maps of the area to gain an understanding of the landscape and/or any special features. Students will need to know that: On the geological map different rock types are shown as different colours The stratigraphic column shows the age relationship of the rocks on the map On a stratigraphic column the oldest rocks are at the bottom of the column the youngest at the top Some geological maps show the solid rock and the Drift deposits. Drift refers to geological material deposited since the end of the last Ice Age. Till (boulder clay), peat, glacial sands and gravels, river alluviums are some examples of Drift, not rock but important deposits particularly for the aggregate industry. Students should already be familiar with the Ordnance Survey maps nomenclature Task Using contour lines an image of the form of the land in the area of the quarry should be made, teachers should ensure students are comfortable with the concept of a 2D image showing a 3D structure, that they understand the relationship between width of spaces between contour lines and the steepness of the land Students draw cross sections using the contours Students draw another cross section from the geology map showing the rocks outcropping at the surface This is superimposed onto the Ordnance Survey cross section Homework Students write a paragraph about each of the rock types identified on their cross section. They then answer the following question: Why is this rock (sediment in the case of sand and gravel quarries) quarried? Teachers information Use this homework to start the second lesson. Answers should identify igneous rocks as crystalline, carbonate rocks as susceptible to chemical weathering or as full of fossils, clastic sedimentary rocks such as sandstones, gritstones or mudstones should have some mention of weathering, transportation and deposition. If the written work is in response to removal of sands and gravels then the depositional environment is important, river or glacial meltwater?

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Slavery's western expansion created problems for the United States. More than eighty years after the federal government's role in protecting the interests of slave Brown's death became known, battles erupted over the westward expansion of slavery. Slavery suppressed wages and stole captured the religious land that could have been used by poor white Americans to achieve independence. Without slavery's expansion and his era, Southerners feared that. The State Capitol needed constant resistance from enslaved men and women. The underground railroad of hideaways and safe houses was used by enslaved men and women as the North gradually abolished human bondage. These freedom seekers were captured and returned. White southerners demanded a national commitment to slavery while northerners appealed to their states' rights to refuse capturing runaway slaves. The nation's economy was powered by slave laborers who provided raw materials for the industrial North. As the United States expanded, the fate of slavery remained at the center of American politics. After decades of conflict, Americans north and south began to fear that the opposite section of the country had taken control of the government. Fears nearly a century in the making at last turned into a bloody war. Slavery's history goes back to antiquity. Prior to the American Revolution, nearly everyone in the world accepted it as a natural part of life. They made a lot of money for the British crown. Wealth and luxury gave rise to seemingly boundless possibilities. The ideological foundations of the sectional crisis can be traced back to the rise of revolutionary new ideals that were given rise to by enslaved workers. Natural-law justifications for slavery began to be reexamined by English political theorists. They did not agree with the idea that slavery was a condition that suited some people. Revolutionaries seized onto the idea that freedom was the natural condition of humankind in the late 18th century. The work of splintering the old order began in the United States, France, and Haiti. The next revolution seemed to be radicalized. One after the other, bold and more expansive declarations of equality and freedom followed. "All men are created equal" was declared by revolutionaries in the United States. The "Declaration of Rights and Man and Citizen" was issued by French visionaries. In 1803, the most startling development occurred. The island's slaves led a revolution that turned France's most valuable sugar colony into an independent country. The beginning of the sectional crisis was marked by the Haitian Revolution. The map shows the percentage of slaves in each county of the slave-holding states in 1860. In the "Black Belt" of Alabama, along the Mississippi River, and in coastal South Carolina, all of which were centers of agricultural production in the United States, the highest percentages are found. The era marked a break in slavery's history despite the clear limitations of the American Revolution. The English and American armies freed thousands of slaves. The turmoil of war was used by many to escape. The antislavery struggle would reignite as a result of the emergence of free black communities. Over a long period of time, the national breakdown over slavery occurred. West was important. As the United States pressed eastward, new questions arose as to whether the lands should be free or slave. The framers of the Constitution didn't do much to help resolve the early questions. The actions of the new government gave better clues as to what the new nation intended for slavery. Vermont was admitted to the Union as a free state and Kentucky as a slave state. Americans made little of the balancing act suggested by the admission of a slave state and a free state. By 1820, preserving the balance of free states and slave states was seen as a national security issue. There were new pressures in the West. The Louisiana Purchase doubled the size of the United States. There were questions as to whether the lands would be made free or slave. The rapid expansion of plantation slavery was caused by the invention of the cotton gin. Many Americans, including Thomas Jefferson, believed that slavery would soon die out despite the booming cotton economy. There was tension with the Louisiana Purchase, but there was no national debate. The debate came quickly. The expansion of plantation slavery in the West was especially important after 1803. The Ohio River Valley was an early fault line in the sectional struggle. Kentucky and Tennessee emerged as slave states, while free states Ohio, Indiana, and Illinois gained admission along the river's northern banks. White supremacy was fostered by borderland negotiations and accommodations along the Ohio River as laws tried to keep blacks out of the West. The exclusionary cultures of Indiana, Illinois, and several subsequent states of the Old Northwest and the Far West were foretold by the so-called Black Laws of Ohio. The largest section of the Louisiana Territory, the Missouri Territory, marked a turning point in the sectional crisis. St. Louis, a bustling Mississippi River town filled with powerful slave owners, was an important trade headquarters for networks in the northern Mississippi Valley and the Greater West. Congress debated Missouri's admission to the Union in the early 19th century to see if the territory would be a slave or free place. New York congressman James Tallmadge wants to abolish slavery in the new state. Congress reached a "compromise" on Missouri's admission, largely through the work of Kentuckian Henry Clay. Maine would join the Union as a free state. Missouri would join the Union as a slave state. Legislators wanted to prevent future conflicts by creating a new dividing line between slavery and freedom in the Louisiana Purchase lands. South of that line, running east from Missouri to the western edge of the Louisiana Purchase lands, slavery could expand. The Missouri Compromise was a turning point in the sectional crisis because it exposed to the public how divisive the slavery issue had become. Newspapers, speeches, and congressional records were filled with the debate. From that point forward, pro-slavery and anti-slavery positions returned to the same points made during the Missouri debates. Legislators battled for weeks over whether the Constitutional framers intended slavery's expansion. "All men are created equal" was a phrase that was disputed all over again. Most Americans concluded that the Constitution protected slavery where it already existed, despite questions over the expansion of slavery. During the Missouri debate, the southerners insisted that the framers supported slavery and wanted to see it expand. The Constitution allowed representation in the South to be based on rules that defined an enslaved person as three fifths of a voter, meaning southern white men would be overrepresented in Congress. Congress was allowed to draft fugitive slave laws after the Constitution stipulated that they couldn't interfere with the slave trade. Participants in the Missouri debate argued that the fram ers never intended slavery to survive the Revolution and that they hoped it would disappear through peaceful means. The framers recognized the flip side of the slave trade debate and opened the door to legislating the end of the trade once the deadline arrived, according to antislavery activists. Slavery could be banned in the territories according to the Tenth Amendment. They pointed to the due process clause of the Fifth Amendment, which said that property could be seized through appropriate legislation. They were a referendum on the American past, present, and future. Despite the furor, the Missouri crisis did not inspire hardened defenses of either slave or free labor as positive good. In the coming decades, those would come. The uneasy consensus forged by the Missouri debate brought a measure of calm. African Americans and Native Americans were troubled by the debate in Missouri. Both groups saw that whites never intended them to be citizens of the United States by the time of the Missouri Compromise debate. The debate over Missouri's admission offered the first sustained debate on the question of black citizenship, as Missouri's state constitution wanted to impose a hard ban on future black migrants. Legislators agreed that the ban violated the U.S. Constitution, but they also agreed that Missouri could deny citizenship to African Americans. Deep fault lines in American society were exposed by The Crisis Joined Missouri's admission to the Union in 1821. A new sectional consensus was created by the compromise that most white Americans hoped would ensure a lasting peace. White Americans agreed that the Constitution could not do much about slavery where it already existed and that it would never happen north of the 36deg30' line. The results proved even more damaging after westward expansion challenged this consensus again. The first to signal their discontent were the enslaved southerners. The rebellion led by Vesey threatened lives and property in the Carolinas. The nation's religious leaders expressed a rising discontent with the new status quo, as well as promoting schisms within the major Protestant churches, which became increasingly sectional in nature. New political parties, new religious organizations, and new reform movements were drawn on by sectionalism between 1820 and 1846. As politics grew more democratic, leaders pandered to a unity under white supremacy by attacking old inequalities of wealth and power. The nation's attention was briefly on slavery in the early 1820s. The last half of the decade saw the return of slavery, and it appeared to be even more threatening. The social change of Jacksonian democracy inspired white men regardless of status to gain the right to vote, attend public schools, and serve in the armed forces. The country's new expansionist desires were pushed in aggressive new directions by leaders. The sectional crisis deepened as they did so. The Democratic Party seemed to offer a solution to the problems of sectionalism by promising benefits to white working men of the North, South, and West, as well as unifying rural, small-town, and urban residents. Huge numbers of western, southern, and northern workingmen supported Andrew Jackson in the presidential election. The Democratic Party sought to unite Americans around shared commitments to white supremacy and desires to expand the nation by avoiding the issue of slavery. Democrats had critics. As the 1830s wore on, more and more Doughfaced Democrats became vulnerable to the charge that they served the south better than they served the north. Whites discontented with the direction of the country used the slur and other critiques to help chip away at Democratic Party majorities. The accusation that northern Democrats were lapdogs for southern slaveholders had real power. The patterns of westward migrations out of New England were mirrored by Whig strongholds. Wealthy merchants, middle- and upper-class farmers, planters in the south and settlers in the Great Lakes made up the Whigs. In the 1830s, the party struggled to convey a cohesive message because of this motley coalition. Their strongest support came from places like Ohio's Western Reserve, the rural and Protestant-dominated areas of Michigan, and similar parts of Protestant and small-town Illinois. A young convert to politics named Abraham Lincoln was one of the figures attracted to these positions. By the early 1830s, Lincoln fit the image of a Whig, as he admired Henry Clay of Kentucky. Lincoln was a veteran of the Black Hawk War and had relocated to New Salem, Illinois, where he lived a life of thrift, self-discipline, and sobriety as he prepared for a professional life in law and politics. Antislavery was never a core component of the Whig platform, despite the party blaming Democrats for defending slavery at the ex pense of the American people. The Whigs were so hated by the abolitionists that they formed their own party. The antislavery Liberty Party was organized in New York. Liberty leaders wanted the end of slavery in the District of Columbia, the end of the interstate slave trade, and the prohibition of slavery's expansion into the West. The Liberty Party distanced themselves from the idea of true racial egalitarianism, as well as shunning women's participation in the movement. Americans did not vote for the party. The Democrats and Whigs dominated American politics. Democrats and Whigs fostered a moment of relative calm on the slavery debate, partially aided by gag rules prohibiting discussion of antislavery petitions. Arkansas and Michigan became the newest states admitted to the Union, with Arkansas coming in as a slave state and Michigan as a free state. Arkansas came in under the Missouri Compromise, but Michigan gained admission through provisions in the Northwest Ordinance. The admission of Arkansas did not threaten the consensus because it was below the line. There was a balancing act between freedom and slavery. The balance would be shattered by events in Texas. Texas gained recognition from the Andrew Jackson administration. Martin Van Buren, Jackson's successor and a Democrat, was worried about the Republic of Texas. Texas had conflicts with Mexico and Indian raids. James K. Polk tried to bridge the sectional divide by promising new lands to whites north and south. As Polk championed the acquisition of Texas and the Oregon Territory, northern Democrats became annoyed with their southern colleagues. The debates over Texas statehood showed that the federal government was in favor of slavery. Houston was admitted to the Union for Texas in 1845 after securing a deal with Polk. Florida entered the Union as a slave state in 1845. The year 1845 was a turning point in the memory of antislavery leaders. As Americans embraced calls to pursue their manifest destiny, antislavery voices looked at developments in Florida and Texas as signs that the sectional crisis had taken an ominous and perhaps irredeemable turn. There were a number of disturbing developments in the 1840s. New personal liberty laws were passed in protest by a number of northern states. The rising controversy over the status of fugitive slaves grew out of the influence of escaped former slaves. The nation's coming sectional crisis was marked by the entrance of Douglass into northern politics. Like many enslaved people, Douglass grew up without knowing his mother or date of birth. As a result of his upbringing, as well as his own genius and determination, Douglass was able to learn how to read and write. He escaped from slavery when he was just nineteen. The book launched his career as an advocate for the enslaved and helped raise the visibility of black politics. Other former slaves, including Sojourner Truth, also supported antislavery, as did free black Americans. They helped thousands to escape from fugitive slave laws. One of the more dramatic examples is the career of Tubman. The forces of slavery had powerful allies. The year 1847 signaled the beginning of a dark new era in American politics. The borders of the nation were to be extended to the shores of the Pacific Ocean and President Polk was eager to see western lands brought into the Union. The administration was blasted as little more than land grabs on behalf of slaveholders. Antislavery complaints seemed to be justified by events in early 1846. After the United States admitted Texas to the Union, Mexico continued to lay claim to its lands. Polk ordered troops to Texas to enforce claims stemming from the border dispute. The United States invaded Mexico City in 1847 after Polk asked for a war. Whigs found their protests unimportant, but antislavery voices were becoming more powerful. The sectional crisis raged in North America after 1846. The new lands would be either slave or free. Slavery was defended as a positive good by the South. The expansion of slavery into the territories won from Mexico was banned by Congressman David Wilmot. The proviso passed the House with bipartisan support, but it failed in the Senate. The conclusion of the Mexican War led to the Treaty of Guadalupe Hidalgo. Antislavery leaders in the United States were upset by the treaty. The Mexican War was judged a slaveholders' plot by antislavery activists. The leaders of the Free Soil Party were aware that the Liberty Party was not likely to provide a home to many moderate voters. The Whigs and the Democrats nominated pro-slavery southerners in that year's presidential election, but the antislavery leaders thought their vision of a federal government divorced from slavery might be represented by the major parties. The leaders of the antislavery Free Soil swung into action. Demanding an alternative to the pro-slavery status quo, Free Soil leaders assembled so-called Conscience Whigs. The national convention was called for in August of 1848. A group of New Yorkers loyal to Martin Van Buren were among the ex-Democrats who committed to the party immediately. The United States acquired territories from Mexico in the 19th century, raising questions about the balance of free and slave states in the Union. The Liberty Party won the popular vote. It was a good start. In Congress, Free Soil members had enough votes to swing power to either the Whigs or the Democrats. The admission of Wisconsin as a free state in May 1848 helped cool tensions after the admissions of Texas and Florida. The news from failed European revolutions alarmed American reformers, but as exiled radicals entered the United States, a strengthened women's rights movement also flexed its muscles. The first of its kind in the U.S., it was chaired by figures such as Elizabeth Cady Stanton and Lucretia Mott, women with deep ties to the abolitionist cause. That is exactly what it did. The spirit of reform didn't make much of a difference at the polls in November. The Whig candidate was bested by the Democrat. The upheavals of 1848 ended quickly. The Mexican War's fruits began to diminish during Taylor's brief time in office. Taylor's administration struggled to find a solution while he was alive. The country was pushed closer to the edge by increased clamoring for the admission of California, New Mexico, and Utah. New states were about to be admitted as thousands poured onto the West Coast and through the trans-Mississippi West after gold was discovered in California. Mormons in Utah made claims to an independent state called Deseret. California wanted to be a free state by 1850. The 1850s were off to a troubling start with so many competing dynamics and the president dead. There was no compromise that could bridge all the interests at play in the country. Clay left Washington discouraged. Stephen Douglas shepherded the bills through Congress. The Great Compromiser, Henry Clay, addresses the U.S. Senate during the debates over the Compromise of 1850. The print shows John C. Calhoun, who was pacified by the Compromise for his increasingly sectional beliefs. The Compromise of 1850 tried to offer something to everyone, but it only made the sectional crisis worse. The package gave the federal government the power to deputize regular citizens to arrest runaways. The New Mexico Territory and the Utah Territory would be able to determine their own fates as slave or free states based on popular sovereignty. territories were able to submit suits to the Supreme Court over the status of fugitive slaves. The admission of California as the newest free state in the Union cheered many northerners, but it wasn't enough. Northerners gained a ban on the slave trade in Washington, D.C., but not the full abolition the abolitionists had advocated. In order for the federal government to absorb some of the former republic's debt, the state of Texas was asked to give some of its land to New Mexico. The compromise debates became ugly. Slaveholders co-opted the federal government and the southern Slave Power secretly held sway in Washington, where it hoped to make slavery a national institution after the Compromise of 1850. The three-fifths compromise of the Constitution gave southerners proportionally more representatives in Congress. Antislavery leaders argued that Washington worked on behalf of slaveholders while ignoring the interests of white working men. The Fugitive Slave Act was the most troubling of the individual measures. In order to extend slavery's influence throughout the country, the act created special federal commissioners to determine the fate of alleged fugitives without the benefit of a jury trial or even court testimony. Local authorities in the North were not allowed to interfere with the capture of fugitives. When called upon by federal agents, Northern citizens had to assist in the arrest of fugitive slaves. An alarming increase in the nation's policing powers is one of the things Act created. The bill undermined local and state laws. The federal commissioners who heard these cases were paid $10 if they determined that the person was a slave and only $5 if they decided he or she was free. The Whigs' existence as a national political party was ended by the presidential election of 1852. The Whigs won just 42 of the electoral votes. Peaceful consensus seemed to be on the horizon with the Compromise of 1850. With a Democratic Party mistake, a coalition against the Democrats may yet emerge and bring them to defeat, as the antislavery feelings continued to run deep. The book tells the story of a woman who escapes slavery using her own two feet, but a man who is chained up and killed by a brutish master. Many Northerners were compelled to join the fight against slavery because of the violence that 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 The book reinforced many racist stereotypes despite the powerful antislavery message. The deeply ingrained racism that plagued American society was a problem for even the abolitionists. Democrats were splintered along sectional lines over slavery, but they had reasons to act with confidence. The bitter fights over the Compromise of 1850 caused voters to return them to office in 1852. The Nebraska Territory, the last of the Louisiana Purchase lands, was supposed to be organized in a bill drafted in the late 19th century. The Nebraska Territory stretched from the northern end of Texas to the Canadian border. In 1854, Douglas's efforts to amend and introduce the bill opened dynamics that would break the Democratic Party in two and rip the country apart. In 1854, Douglas proposed cutting off a large swath of Nebraska and creating a new state called the Kansas Territory. There were a number of goals that Douglas had in mind. The expansionist Democrat from Illinois wanted to organize the territory to make it easier for the completion of the national railroad. Before he finished introducing the bill, the opposition had begun to mobilize. The Kansas-Nebraska Bill was exposed as a measure to overturn the Missouri Compromise and open western lands for slavery by Salmon P. Chase. The Kansas-Nebraska protests took place throughout the North in 1854. Depending on the result of local elections, Kansas would either become a slave state or be free if migrants flooded the state to stop the spread of slavery. Ordinary Americans in the North resisted what they were told was a pro-slavery federal government on their own terms. The rescues and arrests of fugitive slaves Anthony Burns in Boston and Joshua Glover in Milwaukee signaled the rising vehemence of resistance to the nation's 1850 fugitive slave law. Many northerners were radicalized by the Fugitive Slave Law. On May 24, 1854, twenty-year-old Burns, a preacher who worked in a Boston clothing shop, was clubbed and dragged to jail. A group of slave catchers came to return Burns after he escaped slavery in Virginia. A mob gathered outside the courthouse to demand Burns's release after learning of his capture. The federal government sent soldiers to Washington after a deputy was shot in the courthouse two days after the arrest. Boston was placed under martial law. Burns was sent back to slavery in Virginia after federal troops lined the streets of Boston as he was marched to a ship. After spending over $40,000, the U.S. government was able to escort Anthony Burns out of slavery, but the outrage among Bostonians only grew. The federal government imposed the Fugitive Slave Law on northern populations. Anthony Burns, the fugitive slave, is depicted in a portrait at the center of this 1855. The arrest and trial of Burns was possible because of the 1850 Fugitive Slave Act. In the spring of 1854, Burns's treatment caused riots and protests in Boston, as a symbol of the injustice of the slave system. Adams Lawrence said that they went to bed one night old-fashioned, conservative, compromise Union Whigs. The New England grant Aid Company provided guns and other goods for pioneers willing to go to Kansas and establish the territory as antislavery through popular sovereignty as northerners radicalized. Politics became more militarized on all sides of the slavery issue.

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Count in 5s Learn how to count in fives from 0 to 50. This lesson includes: - one video - one activity Let's start this lesson with a physical warm up. Let's count up and down in 5s. For more help and advice with Maths watch this Teacher Talk video. Here is a number grid starting at 1 and finishing with 50. Look at the coloured numbers. What do you notice? Here are the numbers: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. Each number is 5 more than the number before. These flowers all have 5 petals each. - How many flowers are there? - How many petals are there? Count in 5s to help you work out the number of petals. There are 5 flowers with 25 petals in total. Counting in 5s helps you learn to multiply by 5. So, 5 flowers with 5 petals each is the same as saying: 5 x 5 = 25 petals Counting in 5s gives you the 5 times table. Practise counting up in 5s from 0 to 50. When counting in fives, the last digit will always end with either 0 or 5. Play Guardians: Defenders of Mathematica to learn more about this topic and test your skills. There's more to learn Have a look at these other resources.

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Box Plots. Suppose a teacher has given a test to two classes. He would like to know how the marks (data) for each class are spread out. He can compare the two sets of data by drawing a box plot (also called box and whisker plot ).By eilis View Appropriate number line PowerPoint (PPT) presentations online in SlideServe. SlideServe has a very huge collection of Appropriate number line PowerPoint presentations. You can view or download Appropriate number line presentations for your school assignment or business presentation. Browse for the presentations on every topic that you want. Number line. Definition:. It is a line drawn by a ruler and numbered starting with 0 and it is infinite. Distance between numbers must be equal. We use it to represent sets and operations. Examples:. 1) represent the following Sets: a) Finite Sets Number Line. Positive #. Negative #. Origin. Number Line. Example: Locate & label the points on the real number line associated with the numbers -2.5 , +2.5 , 3/4. -2.5. 3/4. +2.5. -3. -2. -1. 0. 1. 2. 3. On your own paper: 1. Draw a horizontal line and place the numbers 0 & -3 on the line. 2. Place the following on your line. * -2 * 2 * 1 * 3 * -1 * -3/4. * -0.75 * -1.2 * 6/5. * -5/3 * 1 1/2 * -6/5 * 1/4 * -2 1/4 * 1.5. Number Line Task. The Number Line. Make your Own Number Line!. Vocabulary. Positive numbers: numbers that are greater than 0. These numbers are located to the right of 0 on a number line. Positive numbers can be written with or without a plus sign. Examples: 3, +3, 5, +6. Vocabulary. Positive and Negative Numbers. The Number Line. -7. -6. -5. -4. -3. -2. -1. 0. 1. 2. 3. 4. 5. 6. 7. 8. Look at the number line above. What numbers go before the zero?. We are now going to use the number line to carry out some calculations. Subtract. -7. -6. -5. -4. -3. Extending the Number Line. 7.NS.1 Integers. Hot and Cold Running Weather. Libya has some of the hottest weather on earth, with temperatures up to 136 ° F. The coldest temperature recorded is at Vostok Station, Antarctica; a freezing −128 ° F. So what is the difference between them?. Basic Subtraction Model. The Ubiquitous Number Line. From Korean Mathematics Book 1-2-1, p 9. Comparison Subtraction Model. The Ubiquitous Number Line. From Korean Mathematics Book 1-1-5 pg 65. Time modeled on Number Line. The Ubiquitous Number Line. Jumping the number line. I am learning to jump through a tidy number on a number line to solve problems like 17 + …. = 91. Numbers like 10, 20, 30, 40 etc. SAMPLE PROBLEM. Out of the 70 books, 37 are comic books. How many are not comic books? ... How many are not comic books? How would you explain why you The Real Number Line. Are you positive about the negatives?. Comparing People’s Heights. GIRLS. BOYS. If you lined up all the students in my class on this line with the shortest students near the vertical line, what would you notice?. Real Number Line.

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In this tutorial, you will learn about computer number system along with its types. Let's start the tutorial with definition of number system. Number system defines a set of value used to represent quantity. Number system is a language of digital system consisting of a set of symbol called digits with rules defined for addition, multiplication and other mathematical operation. Base or radix of a number system is the number of symbol used in its representation. There are four types of number system in general: There are various types of number system available as given in the following table with its base/radix: The decimal number system uses 10 symbols, that are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The binary number system uses only 2 symbols, that are 0 and 1. The octal number system uses 8 symbols, that are 0, 1, 2, 3, 4, 5, 6, 7. The hexadecimal number system uses 16 symbols, that are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. The decimal number system is also called as the base-10 system because it has total of 10 digits to use, that are from 0 to 9. Binary number system is the most important and valuable number system from all the number system for computer point of view. As we all knows that a computer can not operate on the decimal or any other number system because it only operates using binary logic. This number system only uses 2 digits or symbols, that is 0 and 1. Or we can says that this system will only depends/operates on 0 and 1 basis. Octal number system uses digits from 0 to 7, that is total of 8 digits or symbols. This number system uses 16 digits or symbols. In 16 digits, 10 digits are from 0 to 9 and other 6 are from A to F. Now we will talk about conversion from one number system to another number system with its step by step explanation. Here are the list of conversion that are going to be discussed from next tutorial. From next page, you will see all the conversion with its step by step working rule. © Copyright 2021. All Rights Reserved.

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The easiest way to teach students how to choose an operation is to teach them to identify key words. Consider writing this chart below on your front board and have students copy it into their problem solving notebooks. Both of these examples show that a key component of an effective lesson is the balance between individual/group work and the chance for students to share and compare their approaches, strategies, and solutions in presentations to the whole class. Orchestrating this transition, as well as bringing the class period to a close, summarizing the work that has been done, and setting up the next day's extensions, are also key tasks for the teacher. Students may write that they added two plus four because it said “$2 and $4” so they thought that it meant to add. Then, they subtracted $6 from $10 because it said the word “How much” and “Left” and that is how they came to answer of $4. It is also important to encourage students to read the entire problem once through before they choose an operation. In other words, in order to successfully find a solution to the problem, students will need both their reading and mathematical skills. Understanding how to choose an operation can be difficult for many students, especially for students who struggle with reading. This strategy involves deciding which mathematical operation students will use (addition, subtraction, multiplication, division, or a combination of operations). When choosing a mathematical operation, students will need the ability to understand the literal meaning of the sentence, as well as understand how to express the meaning mathematically.

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Tuesday 15th December 2020 LC- To divide fractions. Excellent work so far year 6 on dividing fractions. So we have noticed a link between dividing by a whole number and multiplication. Have a look at the following task. See how many calculations you can make and record these in your books. So, my friend says she can make an equation: 3⁄4 divided by 6 = 1⁄8. Is she correct? How can we check? Method 1 shows how we can use the bar model to help us divide. Can you explain how this is done? Method 2 shows how to use the inverse. For example, dividing by 2 is the same as multiplying by half. Dividing by 3 is the same as multiplying by 1/3. Now let's go through the guided practice together. We will use both methods then see which one you prefer. Now work on Maths NO Problem worksheet 16. Use your preferred method.

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To better comprehend what emotions are, consider their three main components: subjective experience, physiological reaction, and behavioral response. These three components make up the definition of emotion used by psychologists. Subjective experience means how someone feels about something. It includes feelings such as joy, anger, fear, and sadness. Emotions are subjective experiences that come from within a person. Objects or situations may cause these feelings in a person. For example, if someone sees a friend in need, they might feel sad. This is because they know that their friend is experiencing loss or pain. The person who is feeling the emotion does not have to be the one who caused it; they just have to experience it. Physiological reactions occur inside the body when an emotion arises. These physical changes help us deal with threats and find food and shelter. The heart beats faster, blood flows to major muscles, and sweat glands activate when we feel fear. These physical reactions prepare us to act or run away if needed. People often say they "feel like" they are going to be sick because their bodies are reacting physically to this emotion. Behavioral responses are actions taken by individuals to cope with their emotions. They include things like crying, screaming, or hiding. It is suggested that emotions are composed of three components: physical arousal and a cognitive label... A reaction of the entire organism consisting of three components: A complete picture of emotions comprises cognition, physiological experience, limbic/preconscious experience, and even behavior. Let's take a deeper look at these four emotional components. Cognition includes all thought processes and judgments that we experience. It involves understanding what is happening around us as well as thinking about our future goals and plans. Cognitive activities include thinking about thoughts, imagining scenes, making decisions, and solving problems. All emotions involve some type of cognitive processing. For example, when you feel angry, you think about what happened earlier today that made you feel this way. You also might think about possible solutions to your problem. Feeling afraid requires you to analyze potential threats to yourself or others. Your physiology reflects how your body is functioning at any given moment. Your emotions affect your physiology by changing such things as your heart rate, blood pressure, and body temperature. These changes help you to identify what emotion you are feeling. Limbic/preconscious experience refers to all those feelings and sensations that occur below the level of awareness. These are automatic responses to situations that require no cognitive analysis. For example, if someone hurts your friend, you would likely feel fear or anger without thinking about it. Such emotions are called "limbic" because they originate in the brain's emotional center, the limbic system. Here's a breakdown of what each of these five categories entails. Anxiety, rage, guilt, and melancholy are all common emotions. These are impacted by a person's biological basis as well as their experience. They offer a wide range of emotional sensations. Anxiety can be either physical or mental, while depression is a feeling that includes sadness but also irritability, loneliness, and boredom. Anger is a strong emotion that involves a desire to harm another person. It is often felt as hatred towards someone who has offended you or taken advantage of you. Fear is an emotion that causes us to react in order to avoid danger. It is natural for us to feel fear when confronted with something we do not understand, such as when faced with an animal we have never seen before or when standing up to talk to someone we find intimidating. Shame is a feeling caused by our perception that others view us negatively. It can occur when we think others know about our mistakes or failures. Pride occurs when we feel good about ourselves for some reason. It can be experienced as self-esteem or satisfaction. Hating someone would be experiencing anger toward them. Feeling love is seeing someone as valuable and deserving of your affection. Emotions are simply judgments that come quickly after perceptions of risk or reward. This means that emotions are influenced by both biology and experience. Emotions serve as warnings that something may hurt us or help us; they can motivate or guide behavior. What are the three (3) things we are most likely to do when we are feeling good? We may help others by being flexible in our thinking and coming up with answers to our challenges. In addition, we tend to want to share our feelings with others so they know we care and don't take them for granted. Finally, we like to have fun! When you are happy, it is easier to be tolerant of others' faults and mistakes. Your brain's pleasure center gets activated when you do something that makes you feel good. This part of your brain produces chemicals such as dopamine and serotonin that make you want to do it again. These are the reasons why people often say that they "have a habit" of doing certain things. For example, if you drink coffee every day, this isn't a habit - it's a need! The three main activities that activate this center are eating well, drinking enough water, and getting enough sleep. So, the next time you feel good about yourself, remember these three things: eat well, drink enough water, and get enough sleep. Not only will this make you feel even better, but it will also help you think more clearly and act properly too!

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In Excel, the AND operator is used to test whether all of the conditions in a given formula are met. For example, the formula =AND(A1<5,A1>10) would test to see whether the value in cell A1 is less than 5 and greater than 10. If it is, the result of the formula would be "true." If it is not, the result would be "false." The syntax of AND in Excel is as follows: =AND(logical_test, [value_if_true], [value_if_false]) The logical_test argument is a logical expression that is evaluated to true or false. If the logical_test is true, the value_if_true argument is returned. If the logical_test is false, the value_if_false argument is returned. One example of how to use the AND function in Excel is to return the value of a cell if two conditions are met. For example, if you want to find the value in cell A1 if both the value in cell A2 is greater than 10 and the value in cell A3 is less than 20, you can use the following formula: =AND(A2>10,A3<20) There are many instances when you should not use the AND function in Excel. One such example is when you are trying to compare two lists of data and only want to return results that are in both lists. In this case, you would use the Excel OR function instead of the AND function. Another instance when you should not use the AND function is when you are trying to calculate the probability of two or more events occurring. In this case, you would use the Excel OR function instead of the AND function. There are a few similar formulae to AND in Excel. One is called IFERROR. This formula checks to see if a certain condition is met, and if it's not met, it will return a certain value. Another similar formula is called IF. This formula also checks to see if a certain condition is met, but it will return one value if the condition is met and another value if the condition is not met. Lastly, another similar formula is called VLOOKUP. This formula searches through a table of data to find a specific value, and then returns the corresponding value from the table.

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What our Introduction to Atoms lesson plan includes Lesson Objectives and Overview: Introduction to Atoms teaches students about the building blocks of life. Students will discover how billions of these tiny pieces of matter make up their bodies, the oceans, the air, and every other thing. They will learn what components all atoms have and will be able to define them and their functions. This lesson is for students in 4th grade, 5th grade, and 6th grade. Every lesson plan provides you with a classroom procedure page that outlines a step-by-step guide to follow. You do not have to follow the guide exactly. The guide helps you organize the lesson and details when to hand out worksheets. It also lists information in the yellow box that you might find useful. You will find the lesson objectives, state standards, and number of class sessions the lesson should take to complete in this area. In addition, it describes the supplies you will need as well as what and how you need to prepare beforehand. The list of supplies you will need for this lesson includes cotton balls, paint, glue, tape, and other supplies that depend on the method you choose to create models of atoms for the activity. You will also need to gather about 10 items that are very different for the class opening, making sure you have a mix of items that are solids, liquids, and gases. Options for Lesson The “Options for Lesson” section of the classroom procedure page lists several suggestions for additional activities or alternative ways to go about the lesson. A few of these suggestions relate to the activity. For example, you could pair students rather than have them work alone for the activity. You could also use additional materials for the models and have students create models of more than one element. You can assign a specific element to each student to model. As an alternative to the activity, you could have students make 2D models instead, using poster board and other drawing supplies. The teacher notes page provides a paragraph of additional information or guidance as you prepare your lesson. It mentions that the lesson material can range from too simple to too complex. This depends on the level of your students, the curriculum you follow, and the level of understanding you want your students to have. Keep this in mind as you prepare to ensure you deliver a lesson your students will be able to follow. You can also use the lines on this page to write down thoughts or ideas you have before presenting the lesson to your students. INTRODUCTION TO ATOMS LESSON PLAN CONTENT PAGES What Are Atoms? The Atoms lesson plan includes four pages of content. The first page explains what atoms are by defining them as the building blocks that create every single thing in the universe. Without atoms, not a single thing in the entire world would exist! This includes living things, like animals and plants, and non-living things, like air and water. Atoms make up the cells that develop into various living things like animals and plants. Cells are the building blocks of life, but atoms are the building blocks of cells—and everything else. Students will learn that the human body is comprised of billions of atoms. Atoms make up every solid, liquid, and gas that exists. They make up the water we drink, the oxygen we breathe, and the earth we walk on. They are so tiny that they are invisible without a special microscope. Inside every atom are three kinds of particles: protons, neutrons, and electrons. The differences in the number of these particles within the atom determine what that atom can create. A proton is a unit of positive electric charge, an electron is a unit of negative electric charge, and a neutron is a unit with no power. Both protons and neutrons make up the nucleus at the center of an atom. The electrons spin around outside the nucleus in what scientists call the shell. Elements of Atoms Students will next learn about elements. Atoms create elements, and the element an atom creates depends on its number of protons, neutrons, and electrons. There are a total of 120 elements. Scientists use the Periodic Table of Elements to keep track of them and organize them by atomic number and other features. This lesson compares elements to the letters that make up words, with words representing the many things elements have made. When elements join together, they create molecules. A molecule is a particle that contains more than one type of atom. Water is a great example of a molecule made up of different atoms. The two elements that join together to make water are hydrogen and oxygen. A water molecule requires two atoms of hydrogen and one atom of oxygen. Some elements are made up of single atoms and don’t attach to other atoms. Neon is an example of this type of element. However, there are certain atoms that attach to themselves and make a different substance. Oxygen would be an example because it is usually made up of two-atom molecules. The lesson provides a diagram of the Periodic Table of Elements for reference. Here is a list of the vocabulary words students will learn in this lesson plan: - Atom: the building blocks that make up everything in the world - Proton: a unit of positive electric charge within an atom’s nucleus - Electron: a unit of negative electric charge that revolves around an atom’s nucleus - Neutron: a unit of no electric charge within an atom’s nucleus - Nucleus: the center of an atom that contains its protons and neutrons - Element: a substance atoms create depending on how they are organized - Periodic Table of Elements: a table scientists use to keep track of the 120 elements in the world - Molecule: a particle that contains more than one atom INTRODUCTION TO ATOMS LESSON PLAN WORKSHEETS The Introduction to Atoms lesson plan has two worksheets: an activity and a homework assignment. Each of these worksheets will help reinforce students’ comprehension of the lesson material in a different way. The activity in particular provides a hands-on opportunity for students to demonstrate their grasp of the concepts. The guide on the classroom procedure page outlines when to hand out each worksheet to the students. CREATE A MODEL ACTIVITY WORKSHEET For the activity, students will create a model of an atom. They will need a number of supplies to build it, including cotton balls, paint, and heavy stock paper. You will assign each student a specific element for which they will create their atom. (Students can work with partners or in small groups if you prefer.) Students will figure out the correct number of protons, neutrons, and electrons before putting their atom together. Following the directions, students will build the model and connect it to string so that it can hang. INTRODUCTION TO ATOMS HOMEWORK ASSIGNMENT The homework assignment includes a few different sections. First, students will write each of the four parts of an atom using the diagram to the right. Then they will complete 11 fill in the blank questions. At the end, they will define atoms in their own words and explain how they make up everything in the world. Worksheet Answer Key The last page of the lesson plan document is an answer key for the homework assignment. For the most part, students’ responses should mirror those of the answer key. The last question asks students to define atoms in their own words and explain how they make up everything in the world. You will need to review these responses student by students to ensure their answers are accurate. If you choose to administer the lesson pages to your students via PDF, you will need to save a new file that omits these pages. Otherwise, you can simply print out the applicable pages and keep these as reference for yourself when grading assignments.

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F ( N ) Suppose that in the lab one group found that F s x . Construct a graphical representation of force vs. elongation. Graphically determine the amount of energy stored while stretching the spring described above from 0 10 m . Data Set 1 Data Set 2 x ( m ) Graphically determine the amount of energy stored while stretching the spring described above from 0 . 25 m . The graph at left was made from data collected during an investigation of the relationship between the amount two different springs stretched, when different forces were applied. For each spring, use the graph to determine the spring constant. For each spring, use the appropriate math model to compare a. the amount of force required to stretch the spring 3 . 0 m . the E e stored in each spring when stretched 3 . 0 m . Energy WS 3 page 2 5. Determine the amount that spring 2 needs to be stretched in order to store 24 Joules of energy. 6. The spring below has a spring constant of 10 . . If the block is pulled 30 m horizontally to the right, and held motionless, what force does the spring exert on the block? Sketch a force diagram for the mass as you hold it still. (Assume a frictionless surface.) m 7. The spring below has a spring constant of 20 . . The 1 . 0 kg box is pushed to the m right and released, yet remains stationary. The coefficient of static friction s between the box and the surface is 0 . 0 kg a. Draw a force diagram for the box. b. Write an equation for the horizontal forces acting on the box. What is the maximum distance that the spring can be stretched from equilibrium before the box begins to slide back? (Hint: the maximum distance occurs when F fs

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The Reconstruction Era was when Black people flourished and took ownership of their legalized freedom. After the 14th and 15th amendments were passed, this period saw relatively open voting practices. But this was to the detriment of white supremacy. Seeing Black folks participate in democracy and win elections was a threat. So white lawmakers plotted a scheme to suppress Black voters. Southern states created hurdles for Black people to jump over, such as poll taxes and literacy tests, to eliminate the Black vote. But in creating these obstacles, they soon ran into a problem: many white voters–poor and illiterate–couldn’t pay taxes or pass these tests either! The “Grandfather Clause” was created to work around this issue. This clause allowed any person to vote if their father or grandfather was qualified to vote before January 1, 1867. Before this date, free Black people still didn’t have the right to vote – so they were excluded. White people were thus exempt from taxes and tests, but Black people weren’t. The Grandfather Clause was a despicable attempt to quell Black voting power. Many lawmakers today are descendants of those grandfathers–and we still see the disenfranchisement and suppression of Black voters today.

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Compare and Contrast Fictional Characters Students will be able to compare and contrast fictional characters from a familiar story. Students will be able to compare and contrast fictional characters with grade-level words, verb phrases, and adjectives using visuals, sentence frames, and partner support. - Gather students on the rug and ask them to give you a thumbs up if they have ever read or heard of the story, "The Three Little Pigs." - Remind students that the characters in a story are the people or animals in the story. Characters are who the story is about. - Ask students to give you a thumbs up if they know any of the characters in "The Three Little Pigs." - Call on student volunteers to identify the main characters in "The Three Little Pigs"—the three pigs and the wolf. - Remind students that readers have thoughts as they read that help them to understand the story better. - Tell students that today they will be thinking about how the characters in "The Three Little Pigs" are the same, and how they are different.

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What our More About Angles lesson plan includes Lesson Objectives and Overview: More About Angles equips students to apply vocabulary to angles and explore the relationship of angles and their names to a transversal. This lesson also demonstrates the relationship of angle measurement to types of angles. This lesson is for students in 4th grade, 5th grade, and 6th grade. Every lesson plan provides you with a classroom procedure page that outlines a step-by-step guide to follow. You do not have to follow the guide exactly. The guide helps you organize the lesson and details when to hand out worksheets. It also lists information in the blue box that you might find useful. You will find the lesson objectives, state standards, and number of class sessions the lesson should take to complete in this area. In addition, it describes the supplies you will need as well as what and how you need to prepare beforehand. For this lesson, you only need GlueExtra paper for supplies. To prepare for this lesson ahead of time, you can obtain the GlueExtra paper, copy the handouts and other materials, and copy and cut out the pieces needed for the activity worksheet. Options for Lesson Included with this lesson is an “Options for Lesson” section that lists a number of suggestions for activities to add to the lesson or substitutions for the ones already in the lesson. One of the optional adjustments for this lesson is to have students write their own stories as an additional homework assignment. You can also have groups of students create posters for different angles. Students can also practice drawing angles by drawing a picture using only angles and labeling each angle! You can also have the students play win, lose, or draw with each angle and its definition. The teacher notes page includes lines that you can use to add your own notes as you’re preparing for this lesson. MORE ABOUT ANGLES LESSON PLAN CONTENT PAGES The More About Angles lesson plan includes three content pages. The lesson begins with some important vocabulary that students need to know for this lesson. It states that vocabulary is an essential part of learning about angles. Some of the vocabulary words covered in this lesson are congruent, parallel lines, perpendicular lines, and transversal. Each vocabulary word is accompanied by a picture, definition, and symbol (where applicable). Students will learn that congruent means equal or the same. Parallel lines are two lines on a plane that never meet and are equidistant apart. Perpendicular lines are intersecting lines that form right angles. A transversal is a line that intersects a set of parallel lines. The lesson includes a diagram that shows what a transversal is. Relationship of Angles The next section of the lesson teaches students about the different relationships between angles. There are four basic types of angle relationships, which the lesson lists in a chart along with a picture and definition. Complementary angles are when two angles add up to 90 degrees; the two angles do not have to be next to each other. Supplementary angles are when two angles add up to 180 degrees; the two angles do not have to be next to each other. Adjacent angles are two angles that share a common vertex and a common side. Finally, vertical angles are opposite angles made by two intersecting lines. Advanced Relationships of Angles Finally, students will learn about advanced relationships of angles. The lesson explains that we sometimes classify angles based on where they are in relation to a transversal. Students will learn that alternate interior and exterior, corresponding, and same side interior angles all have the same measurements! There are six types of advanced angle relationships, which the lesson lists in a chart along with a definition and examples. Interior angles are angles on the inside of the parallel lines. Exterior angles are angles on the outside of the parallel lines. Alternate interior angles are two angles that are on opposite sides of the transversal and inside (interior) of the transversal. Alternate exterior angles are two angles that are on opposite sides of the transversal and outside (exterior) of the transversal. Corresponding angles are two angles that are in the same place but on different lines. Finally, same side interior angles are two angles that are on the same side of the transversal and on the interior (between) the two lines. The lesson includes a diagram that shows examples of each type of advanced angle. MORE ABOUT ANGLES LESSON PLAN WORKSHEETS The More About Angles lesson plan includes four worksheets: an activity worksheet, a practice worksheet, a homework assignment, and a quiz. You can refer to the guide on the classroom procedure page to determine when to hand out each worksheet. MATCHING GAME ACTIVITY WORKSHEET Students will work either alone or in a group for the activity worksheet. They will match vocabulary terms, their definitions, and drawings that you will cut out and place in a bag for them to use. FOOD COURT PRACTICE WORKSHEET For the practice worksheet, students will use written information about where things are located in relation to each other in a mall food court to fill in the names of the restaurants on the provided diagram. For example, the worksheet states that the SBARRO is located at the alternate exterior angle to the BURGER KING. This worksheet allows students to use what they’ve learned in a new and fun way. They will also have to determine the measurement of each angle on the diagram. MORE ABOUT ANGLES HOMEWORK ASSIGNMENT The homework assignment has two sections. The first section asks students to fill in the missing pieces of a chart that includes relationships, pictures, and definitions. Students will use the given information to fill in the missing sections. The second section of the homework assignment asks students to match types of angles to their definitions. This lesson also includes a quiz. For the quiz, students will use a given diagram to find and answer questions about angles. This quiz will test students’ understanding of the lesson material. Worksheet Answer Keys This lesson plan includes answer keys for the practice worksheet, the homework assignment, and the quiz. If you choose to administer the lesson pages to your students via PDF, you will need to save a new file that omits these pages. Otherwise, you can simply print out the applicable pages and keep these as reference for yourself when grading assignments.

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The dividend is the number we are dividing into. The divisor is the number we are dividing by and the quotient is the answer. A division algorithm is an algorithm which, given two integers N and D, computes their quotient and/or remainder, the result of division. We know that: Dividend = Divisor × Quotient + Remainder Thus, if the polynomial f(x) is divided by the polynomial g(x), and the quotient is q(x) and the remainder is r(x) then f(x) = g(x) . q(x) + r(x). Clearly, if the polynomial f(x) is divided by (x – γ), and the quotient q(x) while the remainder is r the f(x) = (x – γ) . q(x) + r. Division algorithms fall into two main categories: slow division and fast division. Slow division algorithms produce one digit of the final quotient per iteration. Examples of slow division include restoring, non-performing restoring, non-restoring, and SRT division. The Division Algorithm for Integers The division algorithm for integers states that given any two integers a and b, with b > 0, we can find integers q and r such that 0 < r < b and a = bq + r. The numbers q and r should be thought of as the quotient and remainder that result when b is divided into a. Of course the remainder r is non-negative and is always less that the divisor, b. - If a = 9 and b = 2, then q = 4 and r = 1. - If a = 12 and b = 17, then q = 0 and r = 12. - If a = -17 and b = 3, then q = -6 and r = 1. - If a = 18 and b = 6, then q = 3 and r = 0. Division Algorithm for Polynomials If p(x) and g(x) are any two polynomials with g(x) ≠ 0, then we can find polynomials q(x) and r(x) such that p(x) = q(x) × g(x) + r(x) where r(x) = 0 or degree of r(x) < degree of g(x). The result is called Division Algorithm for polynomials. Dividend = Quotient × Divisor + Remainder

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Python provides several built-in functionalities for each purpose. These functions can be utilized through the different modules and libraries that become handy sometimes for each purpose. Likewise, the “math” module is one that contains multiple mathematical operations, such as the “sin()” method assists in finding sine values in radian form. This write-up will describe: - What is “math.sin()” Method in Python? - How to Use “math.sin()” method for Finding Values in Python? What is “math.sin()” Method in Python? In Python, multiple built-in methods are available for performing different operations, such as “sin()”. More specifically, “math.sign” is a built-in math function that provides the functionality of finding the sine values of the parameter passed to it in radian form. To use this function, the Pythons “math” module can be imported into the particular program. The syntax of the “sin()” method is: Here, the math.sin() method outputs the sine value of “x”. How to Use the “math.sin()” Method for Finding Values in Python? The “Math.sin()” method can be used to get the sine value of the input. To understand the working of this particular function, let’s try out the following examples. Example 1: Calculate the “sin()” Value of the Integer Number in Python To calculate the sine value of any integer number, first import the “math” library: Call the “sin()” method with argument through the math.sin()“ statement inside the “print()” function As you can see, the sine value of the provided integer number is displayed below: Example 2: Calculate the “sin()” Value of the Float Number in Python If a user wants to get the sin or sine value of the floating number, first, initialize the “float_value” floating variable with desired floating value and passed to it: Use the “print()” statement with “sin()” method and pass a floating variable to it: Example 3: Calculate the “sin()” Value of the Degree As we know the “sin()” method returns the radian value. However, the calculator returns the degrees. The Python built-in “math” module has the “radians()” function to change the radian value of the “sin()” function into the degree. To change the radian value into the degree, call the “radians()” method with parameters and pass as to the “sin()” function. Then, print the degree value using the “print” statement: The degree of the provided value has been displayed as output: We have elaborated on the Python math.sin() method with examples. The “sin()” method is the built-in function of Python. To use this function, the “math” module can be imported into the particular program that provides the functionality of finding the sine values of the parameter passed to it in radian form. This write-up discussed the usage of Python math.sin() method with examples.

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Using and in Boolean if Statements In this lesson and the next, you’ll see some typical Boolean contexts where an and operator might be used. Boolean contexts typically appear as the conditions in 00:15 These instructions modify the flow of execution in your program, either selecting one section of code or another to be executed or selecting a section of code to be repeated. You can create more effective conditions to direct the flow of your program through the use of expressions which use the Let’s first see an example using the if statement. Here is a simple segment of code that describes a person based on his or her age, following an input statement, which will allow us to test it. To be classified as an adult in this example means to be older than eighteen and up to and including sixty-five. So you need to combine two inequalities, age is greater than age is less than or equal to 65, with the operation and to indicate that an age must meet both conditions to be considered an adult. And you can see other classifications use and to connect inequalities that give lower and upper limits on age to be in that category. 01:23 So in the terminal, you can run this a few times to see each branch being selected. 15 is greater than or equal to 0, but it’s not less than or equal to 9. So the first condition is false. So the program drops to the next condition. 15 is greater than 15 is also less than or equal to 18. Since both these conditions are true, the and of them is True, and the program executes the then code for this conditional, telling us you’re an adolescent. If you try a younger age, here, both of the expressions in the first condition are true: age is greater than or equal to 0 and less than or equal to 02:16 So the entire condition is true, so the child phrase should be output. If you continue this, you can find ages that fit the other two conditions as well. 30 is greater than 18 and less than or equal to 65, putting us in the adult category. 70 makes at least one expression fail in each of the first three conditions. It’s not less than or equal to 9, not less than or equal to 18, not less than or equal to So it’s not until the last expression, > 65, that we get a true condition. In the next lesson, you’ll see expressions using Become a Member to join the conversation.

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You're familiar with several of Python's types including strings, lists, tuples, and dictionaries. You also know how to use a variety of operations, methods, conditional statements, and loops. This lecture isn't about learning any new Python features. It's about solving a problem by exploring several approaches to it and using what you already know. In this lecture, we're going to focus on a single problem. The problem is determining whether a string is a palindrome. A palindrome is a string that is read the same from front to back and back to front. For example, noon and racecar are both palindromes. Before we start to write any code, we need to decide which approach we'll take to solve this problem. We're going to explore several different approaches for determining whether a string is a palindrome. These approaches are called algorithms. An algorithm is a sequence of steps that accomplish a task. For our first approach, we revisit the definition of palindrome. A palindrome is string that is read the same from front to back, and back to front. That means that if we have a string, and we reverse it, it's a palindrome, if the original and the reverse are the same. Let's consider a couple of examples. The first example is noon. Noon, reversed. We're beginning with the last letter in the original, becoming the first letter in the reverse string, and so on. The original string and the reverse string are the same so this is a palindrome. Next, let's look at racecar. We'll begin by reversing the string, the r becomes the first letter followed by a, and the original string and the reverse string are equal, so this is also a palindrome. One more example, dented. We begin by reversing the string d, followed by e. This time, the 2 strings are not the same so this is not a palindrome. Now, we'll take a different approach to solving the same problem. We're going to start this time by splitting the string into 2 halves. We'll then reverse the second half of the string, so o, n will become n, o. We compare the first half of the original string with the second half reversed. If they're the same, the string is a palindrome. We'll do this again for racecar. Racecar has an odd length. So, it's not clear which half the e should belong in. We're actually not going to include it in either. We're going to take the string, half of the string before e and the other half of the string after e, and omit the e altogether. We'll then reverse the second half getting r, a, c and compare the first half of the original with the second half reversed to confirm that it's a palindrome. Finally, we'll do the same thing for dented. We split the string in half, reverse the second path, compare the first half to the second half reversed, and this time they're not the same, so this is not a palindrome. Let's consider one more approach. In this approach, we're going to compare pairs of characters. We'll start by comparing the first character to the last to see whether they're the same. Then, we'll compare the second character to the second last, and we stop when we reached the middle of the string. If all of the pairs of characters are the same, then the string is a palindrome. Let's do the same thing for racecar. We begin by comparing the first character to the last, then the second to the second last, third to the third last, stopping when we reach the middle of the string. All of the pair, pairs of characters are the same, so this is also a palindrome. And finally, dented. In this case, the first two pairs of characters are the same, but the third character is not the same as the third last so this is not a palindrome. There may be other approaches to solving this problem. But these are three that we thought of. In upcoming lectures, we'll discuss some features of algorithms that might make one more desirable than another. For now though, we'll implement all three of these algorithms. Now, let's follow the steps of the function design recipe to implement this function. I'm going to open a new window in which to write the function definition. The first step of the function design recipe involves writing example calls on the function in the doc string. To do this, we need to give the function a name. I'm going to call it, is palindrome. The function will take one string argument, such as noon, and return a Boolean indicating whether that string is a palindrome. In this case, it returns true. It should also return true for the string racecar. And we expect that when is palindrome is call, called with the argument dented, that it will return false. Next, we'll write the type contract. This function takes one string and returns a Boolean. The third step of the function design recipe is writing the header. We're using name is_palindrome, and we need to give a name now to the parameter to this function. I'm going to call it s. The last part of the doc string is the description. This function should return true if and only if s is a palindrome. The last two steps of the function design recipe involve writing the body of the function and then testing the function. We are going to complete those two steps in an upcoming lecture.

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The total solar irradiance (TSI) is a measure of the Sun’s energy output. It fluctuates by 0.2 Wm-2 over 11 year and is therefore a reliable indicator for atmospheric temperature and circulation, particularly in the upper atmosphere. According to Abbot, the downward trend of TSI was correlated with the cooling of the climate. Solar radiation can be used to generate energy in a continuous way. The temperature of the Sun determines its emission rate and wavelength range. This radiation has a high density and is abundant. It is an excellent source to energy for a wide variety of applications. The Sun’s radiation emits approximately 3.8×1011 Watt of energy per second. Only about two-thirds of this radiation reaches Earth, and the rest goes into space. In addition to warming the Earth, solar radiation also has the potential to warm other planets in our solar system. Six experiments are used to monitor the Sun’s radiation. The TSI is measured using NASA’s ACRIM3 satellite and NOAA’s Nimbus7 earth radiation budget. These experiments have been measuring the TSI for the last thirty years. The total solar radiation emitted is almost constant over time. However, fluctuations in the sun’s magnetic activity can be observed. 2001 saw the Sun experience its highest level of magnetic activity. However, it then dropped during the longest-ever solar minimum in more than 80 years. This solar minimum ended in 2009 and is currently in a decreasing phase. This pattern is expected continue until at most 2020. Changes in absorbing, scattering and total losses Three processes modify the radiation from the sun that travels through the Earth’s surface. These processes occur when radiation interacts and is suspended with gases. First, radiation undergoes absorption as small particles diffuse the light. This reduces the amount sunlight reaching the Earth’s surfaces. The wavelength and size of the particles can influence the amount of insolation. The atmosphere also reduces the power from solar radiation that falls on the Earth. The amount and quality of the atmosphere’s dust and air molecules will determine the scattered light. If there was no atmosphere, then the sky would be blank and the sun would only be visible as a circle. Finally, the atmospheric composition changes can cause local variations of the incident solar energy. For example, cloud cover that is heavier than usual reduces incident solar power. Both the Earth’s and vegetation’s surface temperatures can be affected if there is an increase in solar radiation. This is particularly true in the northern part of the hemisphere, where slopes face south. The slope has a greater absorbing capacity than a slope facing north. Tillage implements can also be used to modify the slope of a field. A tillage furrow directed east-west will create an uneven surface which will lead to higher soil surface temperatures. Changes to the amount of energy absorbed into the atmosphere are related to changes in absorbing, scattering and total losses caused by increased solar radiation. The Earth’s atmosphere absorbs around 19 units solar radiation and 111 units forfrared radiation. 51 units of energy are absorbed by the surface. TSI’s effect on solar radiation Significant variations in solar radiation from TSI have occurred over the past 9000 years. The quiet solar luminosity, for example, has seen a millennial-scale variation during Maunder minimal. Significant variation in heliospheric activities is also evident during this period of almost no sunspots. TSI proxy simulations reproduce large TSI variation during this time period. They range from 3 to 6. W/m2. The positive correlations found between TSI and solar activities cycles in combined TSI measurements taken by the ERBS experiment as well as the ACRIM1 experiment are clear. Despite the fact the solar activity has declined by a factor 2 over the last ten years, the TSI-trend has remained within +0.05 Wm-2 over the past 21 year. Although this is a slight decrease in the 21 year average, it is still significant due to the reductions in the TSI amplitude (from the maximum to the lowest of cycle 24). TSI sensors have a two-ppm accuracy and can detect changes to total solar irradiance. They are also capable of detecting variations induced by the most powerful X-class solar flares. To further analyze TSI measurement, a robust algorithm was developed to calculate radiative output. This algorithm can be used to account for both impulsive TSI measurements. We used data from four solar flares for comparison, including the 2006 December 6th flare. The solar variability is a significant component of the energy conservation equation for the Earth system. It does have an effect on the climate, but it is unlikely that it will directly affect global temperature. It also influences TSI indirectly, amplifying the effects of direct solar forcing.

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a⁰ = 1 can also be written as a¹⁻¹ = 1 a¹ * a⁻¹ = 1 And as we know that when anything is divided by itself the answer is 1. So if any number is raised to the power of 0 answer would be 1. Any number raised to the first power is always equal to itself. And if the power further increases it describes how many times that number need to be written and multiplied. In order to add or solve binomials we first convert them into monomials need to solve the brackets and multiply all the terms in bracket with the number multiplied to bracket if there is no number than we would consider it as 1. Then after that simplify all the terms or monomials. While simplifying one rule is followed that the terms contain the same variable and exponent can only be added or subtracted. If power of variable which already contains an exponent is taken it means to write the variable with that exponent that many times and multiplied. If the variable does not contain an exponent than we would take it as 1. The same result can also be achieved if we just multiply the exponent and power and male a single exponent of variable While solving monomials one rule is to be followed only those terms with same variable and exponent could be added or subtracted. When same variables are multiplied there powers always add. The variables are need to be same but there exponent could be different A term can be a number or multiplication of number and variable or multiplication of number and variable with exponent. And the number of these terms describes monomial, binomial, trinomial and polynomial If two different variables are divided and power of whole fraction is taken then the same power would be applied to both the numerator and denominator. If two different variables are multiplied and there whole power is taken. Then power would be applied seperately to both variables. If position of variable with an exponent is changed from numerator to denominator or denominator to numinator the sign of exponent would change. When the term would be in new position it would multiply with other term in that part of fraction. And if the terms are with the same variable then there exponent would add up or subtract.

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9. Rocks are classified according to how they are formed. From the diagram above, we can see • Igneous rocks are formed by the cooling or solidification of magma or lava. • Metamorphic rocks are formed by preexisting rocks that are exposed to extreme heat and pressure in the Earth’s interior, a process • Sedimentary rocks are formed by the compaction and cementation of sediments, a process 10. Igneous rocks are formed by the cooling or solidification of magma or lava. • Igneous rocks are further classified as intrusive or extrusive igneous based on grain size. Intrusive rocks, or plutonic rocks, are igneous rocks formed underneath the earth. They are coarse-grained due to the slow cooling of magma allowing crystal Extrusive rocks, or volcanic rocks, are igneous rocks formed on the surface of the earth. They are cooled lava, which are molten rocks ejected on the surface through volcanic eruptions. They are fine-grained due to abrupt cooling on the surface. 11. Igneous rocks can also be classified based on grain size, general composition, and percentage mineral composition. The diagram below shows the four general compositions of igneous rocks–light- colored or felsic, intermediate, dark- colored mafic, and ultramafic. 13. Sedimentary rocks are classified into clastic or non-clastic. Clastic sedimentary rocks are made up of sediments from preexisting rocks. When preexisting rocks are physically weathered and eroded, they form sediments. When these sediments are transported, deposited, and lithified, they form the clastic sedimentary rocks. These rocks can be identified based on their grain sizes that can range from 0.002 mm (e.g. clay size) to > 2 mm (coarse gravel). 15. Non-clastic sedimentary rocks can be biological, chemical, or a combination of both. Biological sedimentary rocks are lithified accumulation of dead organisms. Examples include coal (formed from carbon-rich plants) and limestone (formed from the remains of calcareous organisms). On the other hand, chemical sedimentary rocks are from chemical precipitation. An example is rock salt formed when dissolved salts precipitate from a solution. Below is a table of chemical sedimentary rocks based on composition and texture size. 17. Metamorphic rocks can be classified as foliated or non-foliated based on texture. • Foliated metamorphic rocks have layered or banded appearance produced by exposure to high temperatures and pressures. Examples include slate, phyllite, schist, and • In contrast, non-foliated metamorphic rocks do not have layered appearance. Examples include marble, quartzite, and 18. Foliated and non-foliated metamorphic rocks can be further classified based on their parent rocks. However, such classification can be difficult because of the rock alteration during metamorphism. The table below shows the parent rocks of different foliated and non-

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Established in Article I of the Constitution, the legislative branch has both the power and duty to legislate. Commonly known as Congress, the legislature is often described as the centerpiece of national representative democracy because the people elect legislators. Congress includes the House of Representatives, the body representative of the relative population of the states, as well as the Senate, which represents states equally. Legislators elected to the House of Representatives serve in 2-year terms, while elected senators serve in 6-year terms. While there are only two senators per state, the number of legislators elected to the House of Representatives varies per state as it is determined by population. According to the Constitution, the enumerated powers of Congress include the ability to make laws, lay and collect taxes, regulate both interstate and foreign commerce, declare war, and make all laws necessary and proper to carry out the enumerated powers.

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esl essentials for busy teachers rate this category 64 FREE Word Order Worksheets Recommended worksheets in Word Order: Articles about Teaching Word Order: Word Order WARMERS: GRAMMAR TIP:What Is Word Order? In linguistics, word order typology refers to the study of the order of the syntactic constituents of a language, and how different languages can employ different orders. Correlations between orders found in different syntactic subdomains are also of interest. The primary word orders that are of interest are the constituent order of a clause—the relative order of subject, object, and verb; the order of modifiers (adjectives, numerals, demonstratives, possessives, and adjuncts) in a noun phrase; and the order of adverbials. Some languages have relatively restrictive word orders, often relying on the order of constituents to convey important grammatical information. Others, often those that convey grammatical information through inflection, allow more flexibility which can be used to encode pragmatic information such as topicalisation or focus. Most languages however have some preferred word order which is used most frequently... When you students struggle with word order, take the time to review this with them using one of the 64 word order worksheets available in this section. Browse through this section to find something that your students will enjoy or use these worksheets as a basis for your own. Here is a resource to refer to when talking about word order . The material may be a little overwhelming for your students but the scrambled sentences on the last three pages can be great practice if students have difficulties with word order. There are other scrambled sentences and word order worksheets to look at as well as an article that talks about teaching word order so stick around and explore all that Busy Teacher has to offer. There are many common word order mistakes that English language learners make even as their overall fluency and level increase. You cannot stress the importance of word order enough so be sure that students understand the position of words in a target structure before sending them off to do practice activities. Not everyone supports the idea of giving students incorrect material but this would be one method of checking to see if students understand correct word order. You could create a worksheet with some incorrect sentences and ask students to make corrections to them. To make this more challenging, ask students to correct the incorrect sentences and include some sentences without errors so they have to be even more attentive when reading. Of course the best method of teaching word order is to include it in your introductions; take preventative measures when it comes to word order and you will have fewer problems to deal with later on in the course. ... More About... Less About Recently added worksheets in Word Order: A thorough and comprehensive peer-editing or self-editing worksheet for essays that covers organization, quality introduction, conclusions, developed body paragraphs as well as grammar issues such ... There are two exercises on the worksheet. The first exercise is a quiz. Students have to identify words in an alphabetic string. In the second exercise students have to put words in the correct or ... This English worksheet can be used when teaching students about Valentine's Day and for alphabetical order. Students look at the words and write them in alphabetical order. There are 15 words for ... This worksheet can be used when teaching children about Valentine's Day. Students must look at the words and unscramble them correctly by writing them on the lines. There are nineteen words to uns ... This worksheet helps my students to learn the correct order of English adjectives. When we group adjectives together there is a general rule for the position of each type of adjectives. These exer ... A quirky, magical tale following the creation of a wooden aviator and his plane. After the death of his inventor, an elderly toymaker, Flyboy is left in the back garden of the house on the hill as ... This worksheet is a mid-term test for beginners. There are two parts:a language part and a spelling part. In the former they can practise vocabulary with a blank filling activity or grammar with m ... This is a worksheet I usually use at the beginning of the school year. The aim is for the students to be able to fill in the information about themselves so later they can write about it. It will ... This page can be folded in half length-wise and torn. Give students the right half so they can try to change the word order of each line to make a sentence. Later, give them the left half so they ... Got a great worksheet on Word Order? Tell us about it and become a BusyTeacher contributor! Submit a Worksheet

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Last week, in Number Sense 31, we made a graph of a more continuous function: how much grass a herd of goats might eat each hour. We also took a look at what the graph might look like if it were an inequality, rather than a strict equality. This week we are going to solve a problem using a graph. Last week we introduced a herd of goats. Why are we keeping goats, anyway? They are cute, that's true, but they are also a lot of trouble. Well, in addition to the pleasure of their company, we get goat milk. It's a herd of dairy goats. Our herd produces 20 liters of goat milk per day. We use some of it as liquid milk: some goes in our coffee, some we drink, some we feed to the baby goats. We use the rest of the milk to make cheese. Here is our first equation: Liquid milk + cheese milk = 20 liters If we call liters of liquid milk “x”, and liters of cheese milk “y” then x + y = 20. We also know that we use more milk to make cheese than we use as liquid milk, and we have measured how much more: 4 liters. Here is our second equation: Cheese milk - liquid milk = 4 liters y – x = 4 We want to know how much milk is used to make cheese every day. We can use these equations to put two lines on the same graph We can make a T chart for the first equation, x + y = 20 and we will pick x = 0 and x = 20 for our x values, which makes figuring out the y values super easy, since the two numbers must add up to 20. Here is the graph of the different amounts of milk we could use for cheese and as liquid milk, given that the total amount of milk is 20 liters. If you check any spot on that line: (18, 2), (10,10), where ever... the two numbers add up to 20. Now we will make a T chart for our second equation y – x = 4 We will pick x = 0 and x = 10 for our t chart values, again choosing numbers that make y easy to calculate We plot these two points on our graph, and draw a line that goes through both points The green line shows all the solutions to cheese milk is four more liters than liquid milk, including the extreme case of zero liters of liquid milk. If we add up the total liters of milk using the green line, we will get different amounts of milk. The spot where the green line crosses the red line, though, it the spot where the total number of liters is 20. That says we use 12 liters of milk for cheese, 8 liters of milk as liquid milk. 12 + 8 = 20, so our first condition (20 liters per day) checks out. 12 – 8 = 4, which satisfies our second condition (four more liters used to make cheese). Have fun in the comments

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In this rounding numbers worksheet, students review how to round numbers and then practice by rounding the first set of numbers to the nearest ten using the number line. Students then round the second set of numbers to the nearest ten. 4th - 5th Math 3 Views 5 Downloads Formative Assessment Task: Number and Operations in Base Ten Engage your class in developing their understanding of place value with this simple hands-on activity. Presented with a multi-digit number, young mathematicians use the provided digit cards to create numbers in response to a series of... 3rd - 5th Math CCSS: Designed Round to the Nearest Hundred Using a Number Line Using a number line to round to the nearest hundred is a snap after watching this video. This sixth of eight videos walks through a review explanation of benchmark numbers, rounding, and midpoints. It then gives several examples of how... 5 mins 2nd - 4th Math CCSS: Designed Round to the Nearest Hundred Using Base Ten Blocks Base ten blocks form the basis of understanding in this lesson on rounding to the nearest 100. A review of place value and finding midpoints on a number chart precedes two examples of rounding a three-digit number. This is the seventh in... 4 mins 2nd - 4th Math CCSS: Designed

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Combinations and Sequences In this combinations review worksheet, students answer 5 multi-step short answer questions involving combinations. Students then answer 15 questions regarding combinations, sequences, and terms. Students also answers 15 probability questions. 4 Views 5 Downloads New Review Permutations and Combinations Counting is not all it adds up to be — sometimes it involves multiplying. The lesson introduces permutations and combinations as ways of counting, depending upon whether order is important. Pupils learn about factorials and the formulas... 10th - 12th Math CCSS: Adaptable New Review Congruent Triangles Is this enough to show the two triangles are congruent? Small groups work through different combinations of constructing triangles from congruent parts to determine which combinations create only congruent triangles. Participants use the... 9th - 11th Math CCSS: Adaptable

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Algebraic Terms Sixth and Seventh-Graders Encounter A dozen things for sixth and seventh grade teachers to keep in mind: - Using Symbols: Symbols have previously been used in formulas provided for specific applications (e.g., A=s² for the area of a square) or as placeholders for unknown numbers in simple arithmetic equations (e.g., “9 = ? + 4”). Now we will extend these ideas to solving more complicated equations, to creating formulas for specific problems, and to modeling co-variation, where two variables change together in a way that keeps an equation true. - Exponent: We introduce notation with integer exponents at this level both for its direct value in arithmetic (in writing factorizations, for example) and to prepare for its use in algebraic expressions. However, we do not address algebraic equations with exponents until later grades. - Expression: An arithmetic expression consists of a set of numbers connected by operation symbols (e.g., +, −, ÷), perhaps with some parts arranged as fractions or as exponents. An algebraic expression is the same except that some numbers may be replaced with letters. - Equation: An equation is a statement that the values of two expressions are equal. - Inequality: An inequality is a statement that the value of one expression is larger or smaller than that of another. - Solving: The solution of an equation or inequality is a description telling which values of the variable make it true (e.g., x = 3 is the solution of 5x + 3 = 18). Note that an expression (such as 3x + 2 by itself, which contains no equals or inequality sign) cannot have solutions because it is not a statement claiming that something is true. - Variables: Arithmetic rules still apply in algebraic expressions, but we can use single-letter symbols wherever we can use numbers. We call these letters "variables" because different numbers may be substituted for them. A variable is called an unknown if we are trying to find a value that will make the statement containing the variable true. - Constants and coefficients: The numbers in an expression are called constants, since their values will stay the same. Numbers that directly multiply variables are called coefficients. For example, the expression 7x + 9 includes the coefficient 7, the variable x, and the stand-alone constant 9. - Implied multiplication: The most obvious change in notation in algebra is that the multiplication sign is almost always omitted in algebraic expressions. When numbers or symbols are not separated by some other operation symbol, they are multiplied together. So 235xy means the same thing as 235 × x × y, and 2(x + 3) means the same as 2×(x + 3). - Factors: A factor is an item that is multiplied by another item. The 235xy expression above consists of three factors: 235, x, and y. The expression 2(x + 3) has two factors: the number 2 and the term (x + 3). - Terms: The word “term” in algebra refers to items or groups of items separated by plus or minus signs. Each term may contain factors and/or items with exponents. Thus the expression 3x² − 2x + 5 has three terms: 3x², −2x, and 5. A term with no variables, like the 5 in this example, is often referred to as a “constant term," or sometimes as just “the constant." - Parameters: When constants in an equation play roles (such as a price or starting point) that might have different values in similar situations, they are sometimes called parameters. For example, we can think of the formulas c = 1.85w and c = 2.45w, which compute cost from weight, as special cases of a general c = pw formula, where p is a price-per-pound parameter. In these cases, p = 1.85 and p = 2.45.

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Esl printables, the website where english language teachers exchange resources: worksheets, lesson plans, activities, etc our collection is growing every day. Students examine linking words and phrases in the text owen and this should give an overview of the lesson plan lesson 14: connecting ideas with linking words. Lesson plan lesson planning a lesson plan is a daily plan usually written as an outline or detailed statement by the teacher for the purpose of teaching students. Find linking words lesson plans and teaching resources from esl grammar linking words worksheets to writing skills linking words videos, quickly find teacher-reviewed educational resources. Reading lesson plans: pearls by jackie mcavoy reading skills including understanding vocabulary in context and summarizing the text with appropriate linking words. This lesson plan for the immigration: stories of yesterday and today interactive online unit exposes students to the unique contributions of immigrants to american histor. Summary an introductory lesson about conjunctions and how they are used a master list of conjunctions is provided for future reference objectives. Conjunctions exercise some exercises to revise connectors of addition and contrast in order to improve student´s writing. I found “using time connectors to build story tension” lesson plan at share my lesson there are so many more free, quality lessons on the site, so head on over. Esol lesson plans skills for life linking words 1 by will forsyth a british english worksheet to complete the sentences using the correct linking words. Use this studycom lesson plan to guide your instruction on comparing and contrasting in addition, find an activity to help them practice the. First lesson:the sentence connectors-additional, sequence, contrast the sentence connectors-additional a lesson plan format -halladocx. Posts about linkers menu about us tim's free english lesson plans use them, share them, comment on them, and share my link in return tag: linkers posted in. What kinds of connectors are used lesson 7: aim – students will plan speeches to persuade others lesson plan. A new lesson plan on linking words my response to requests from my learners for input and practice on linking words. Grammar lesson for upper-intermediate level students focusing on the use of paired conjunctions in both spoken and written lesson plans focusing on tenses and. Use basic connectors (and, but, so, or) to join ideas in simple and complex sentences pay attention to today’s lesson plan 2: 10 min: short quiz. Ks1 english lesson plan and worksheets on conjunctions. Joiners and connectors joiners and connectors lesson plan worksheet activity 8 parts of speech lesson search categories social studies language arts. Sample lesson plan on conjunctions - free download as pdf file (pdf), text file (txt) or view presentation slides online sample lesson plan on conjunctions for high school students. Linking words help you babe barnett thank you so much ,excelent lesson plan and would be nice if you can add some more rare linkers or connectors that can be. Comma in compound sentences lesson plans conjunctions: fan boys and you conjunctions are important for linking two ideas in a cohesive and fluid way. Lesson plan for teaching linking words in business linking words and connectors, modal verbs skills documents similar to the missing link_linking words. Free esl/ efl lesson plan for english teachers - intermediate/ upper intermediate english lesson - linking words ( due to, because, however, etc. Free and exciting new ideas from our creative department download and print out fun instructions to spark your creative straws and connectors play time. A compilation of immigration related lesson plans from across the library's web site. Linking is when sounds are joined together or when a sound is inserted between two others to make them easier to say. In this lesson you will learn how to make your writing flow smoothly by adding linking words and phrases. Explanation on the use of linking words and phrases english grammar for esl learners linking words and phrases back to lesson list. Lesson plan instructor anthony schmidt and by the end of the lesson, begin drafting their which connectors are followed by a noun or noun phrase. The best resource and help for esl, efl and english students and teachers we have free english lessons, free lesson plans and can correct your essays, reports.

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By Tia K. Lewis on May 08 2018 10:36:01 When teaching decimal numbers, first review the basics of thousands, hundreds, tens and ones and then introduce (or review) tenths, hundredths and thousandths. In KS2 children are taught that decimals are another way of writing fractions. The hundred number square is a really good way of showing children the equivalence between fractions and decimals. Children usually start to learn about decimals in Year 4. The first thing children need to know is that a decimal is A PART of a whole. A good way to explain this is to show them an empty hundred number square / chart. These worksheets can help your students review decimals number concepts. Worksheets include place value, naming decimals to the nearest tenth and hundredth place, adding decimals, subtracting decimals, multiplying, dividing, and rounding decimals.

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1.2 The Burgess Shale High in the Canadian Rockies is exposed a deposit of middle Cambrian age, about 530 Ma old, called the Burgess Shale. It contains the fossils of animals that lived on a muddy sea floor, and which were suddenly transported into deeper, oxygen-poor water by submarine landslides. Their catastrophic burial has given us an exceptional view of Cambrian life. Not only have animals with hard shelly parts been preserved but entirely soft-bodied forms are also preserved as thin films on the sediment surface. Before going any further, click on 'View document' below and read pages 62-65 from Douglas Palmer's Atlas of the Prehistoric World. Some of the most common Cambrian fossils, which appear immediately after the first shelly fossils, are trilobites. These were a group of exclusively marine arthropods, members of the enormously diverse phylum of animals with jointed, external skeletons that today include forms such as crabs, lobsters, insects and spiders. The trilobite fossils of the Burgess Shale are like many trilobites found elsewhere but exceptional in that not only is the main part of their outer skeleton (or exoskeleton) preserved, but so too are their appendages such as antennae and legs (see, for example, those of Olenoides, Atlas, p. 63). Elsewhere, trilobite appendages are extremely rare as they were poorly mineralised. We will study trilobites in more detail shortly. Other types of arthropods, especially ones lacking well-mineralised exoskeletons (such as Marrella, Atlas, p. 64), are particularly abundant in the Burgess Shale. Only about 15 per cent of the 120 genera present in the Burgess Shale are shelly organisms such as trilobites and brachiopods that dominate typical Cambrian fossil assemblages (fossils that occur together) elsewhere. The shelly component was therefore in a minority, and organisms with hard parts probably formed less than 5 per cent of individuals in the living community. If the soft-bodied fossils of the Burgess Shale are taken away, all that remains is a typical Cambrian assemblage of hard-bodied organisms. Why is this important to bear in mind when trying to interpret other Cambrian fossil assemblages? The other Cambrian assemblages may also have been dominated by soft-bodied animals, even if the only fossils they now contain are of hard-bodied ones. Another important revelation of the Burgess Shale lies in the wide diversity of animal types that were around in middle Cambrian time, about 530 Ma ago. There are representatives of about a dozen of the phyla that persist to the present day. One form closely related to early arthropods was Anomalocaris, the largest known Cambrian animal, some individuals of which may have reached two metres in length. Its extraordinary jaw (Atlas, p. 65) consisted of spiny plates encircling the mouth, which probably constricted down on prey in much the same way that the plates of an iris diaphragm cut down the light in a camera. This fearsome mouth is seen in place in the reconstruction of the closely related Laggania (Atlas, pp. 64-65). Note that the colours of organisms shown in this and other such reconstructions are conjectural. About a dozen types of Burgess Shale fossils have been said to be so unlike anything living today and so different from each other that, had they been living now, each would have been placed in a separate phylum. With further study, however, the relationships of these puzzling animals (such as Hallucigenia, Atlas, p. 63) are becoming clearer. It seems that some Burgess Shale forms are hard to classify simply because the boundaries between major categories of animal life were still blurred shortly after the Cambrian explosion. In other words, by mid Cambrian time, there still had not been enough time for some groups to have diverged sufficiently from their recent common ancestors to be distinctly different. Burgess Shale-type faunas have been found in about 30 sites ranging from North America and Greenland, to China and Australia. The wide range of animals they contain seems to reflect an unpruned 'bush of diversity' resulting from the Cambrian explosion. Not long after, though, extinction lopped off some of the branches, leaving phyla with the relatively distinct features that have remained to this day.

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In this video I show you how we can use tables to calculate probabilities of being less than or greater than various z values. This works because this table is symmetric about the y-axis. In order to properly use this for calculations, though, one must begin with the value of your z-score rounded to the nearest hundredth. To do this, drop the negative sign and look for the appropriate entry in the table. For example, we could ask for a randomly distributed variable. For this, we would use the. A statistician would then locate 1. The next step is to find the appropriate entry in the table by reading down the first column for the ones and tenths places of your number and along the top row for the hundredths place. Remember that data values on the left represent the nearest tenth and those on the top represent values to the nearest hundredth. A continuous random variable X follows a normal distribution if it has the following probability density function p. We use the following trick: If X ~ N m, s 2 , then put: It turns out that Z ~ N 0, 1. The standard normal distribution Z~N 0,1 is very important as I showed you previously, all normal distributions can be transformed to it. . Another use of this table is to start with a proportion and find a z-score. Note that it is s and not s 2 on the denominator! Use this table in order to quickly calculate the probability of a value occurring below the bell curve of any given data set whose z-scores fall within the range of this table. After locating the area, subtract. Look in the and find the value that is closest to 90 percent, or 0. Normal distributions arise throughout the subject of statistics, and one way to perform calculations with this type of distribution is to use a table of values known as the standard normal distribution table. Sometimes in this situation, we may need to change the z-score into a random variable with a normal distribution. Instead, we convert to the standard normal distribution- we can also use statistical tables for the standard normal distribution to find the c. The mean is 4 and s is 3 the square root of 9. These two values meet at one point on the table and yield the result of. This occurs in the row that has 1. What z-score denotes the point of the top ten percent of the distribution? From this we then evaluate probabilities. Take for example a z-score of 1. One would split this number into 1. Standard Normal Distribution Table The following table gives the proportion of the standard normal distribution to the left of a. The standard normal distribution table is a compilation of areas from the , more commonly known as a bell curve, which provides the area of the region located under the bell curve and to the left of a given z-score to represent probabilities of occurrence in a given population. We write X ~ N m, s 2 to mean that the random variable X has a normal distribution with parameters m and s 2. Negative z-Scores and Proportions The table may also be used to find the areas to the left of a negative z-score. Anytime that is being used, a table such as this one can be consulted to perform important calculations. In this instance, the normal distribution is 95. The normal distribution is symmetrical about its mean: The Standard Normal Distribution If Z ~ N 0, 1 , then Z is said to follow a standard normal distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Io has a density of 3. Galileo 's magnetometer failed to detect an internal, intrinsic magnetic field at Io, suggesting that the core is not convecting. Unlike Earth and the Moon, Io's main source of internal heat comes from tidal dissipation rather than radioactive isotope decay, the result of Io's orbital resonance with Europa and Ganymede. The resonant orbit also helps to maintain Io's distance from Jupiter; otherwise tides raised on Jupiter would cause Io to slowly spiral outward from its parent planet. The friction or tidal dissipation produced in Io's interior due to this varying tidal pull, which, without the resonant orbit, would have gone into circularizing Io's orbit instead, creates significant tidal heating within Io's interior, melting a significant amount of Io's mantle and core. The amount of energy produced is up to times greater than that produced solely from radioactive decay. Although there is general agreement that the origin of the heat as manifested in Io's many volcanoes is tidal heating from the pull of gravity from Jupiter and its moon Europa , the volcanoes are not in the positions predicted with tidal heating. They are shifted 30 to 60 degrees to the east. The movement of this magma would generate extra heat through friction due to its viscosity. The study's authors believe that this subsurface ocean is a mixture of molten and solid rock. Other moons in the Solar System are also tidally heated, and they too may generate additional heat through the friction of subsurface magma or water oceans. This ability to generate heat in a subsurface ocean increases the chance of life on bodies like Europa and Enceladus. Based on their experience with the ancient surfaces of the Moon, Mars, and Mercury, scientists expected to see numerous impact craters in Voyager 1 's first images of Io. The density of impact craters across Io's surface would have given clues to Io's age. However, they were surprised to discover that the surface was almost completely lacking in impact craters, but was instead covered in smooth plains dotted with tall mountains, pits of various shapes and sizes, and volcanic lava flows. - Zimbabwe Science News. - jsclater's web site? - Mission to Mars. This result was spectacularly confirmed as at least nine active volcanoes were observed by Voyager 1. Io's colorful appearance is the result of materials deposited by its extensive volcanism, including silicates such as orthopyroxene , sulfur , and sulfur dioxide. Sulfur is also seen in many places across Io, forming yellow to yellow-green regions. Sulfur deposited in the mid-latitude and polar regions is often damaged by radiation, breaking up the normally stable cyclic 8-chain sulfur. - The Secret To That Takeaway Curry Taste! - Recommended for you. - Terrestrial Heat Flow in Europe - Vladimir Cermak, L Rybach - Häftad () | Bokus. - Terrestrial Heat Flow through Salt-Marsh Peat.. This radiation damage produces Io's red-brown polar regions. Explosive volcanism , often taking the form of umbrella-shaped plumes, paints the surface with sulfurous and silicate materials. Plume deposits on Io are often colored red or white depending on the amount of sulfur and sulfur dioxide in the plume. These red deposits consist primarily of sulfur generally 3- and 4-chain molecular sulfur , sulfur dioxide, and perhaps sulfuryl chloride. Compositional mapping and Io's high density suggest that Io contains little to no water , though small pockets of water ice or hydrated minerals have been tentatively identified, most notably on the northwest flank of the mountain Gish Bar Mons. The tidal heating produced by Io's forced orbital eccentricity has made it the most volcanically active world in the Solar System, with hundreds of volcanic centres and extensive lava flows. Io's surface is dotted with volcanic depressions known as paterae which generally have flat floors bounded by steep walls. One hypothesis suggests that these features are produced through the exhumation of volcanic sills , and the overlying material is either blasted out or integrated into the sill. Lava flows represent another major volcanic terrain on Io. Magma erupts onto the surface from vents on the floor of paterae or on the plains from fissures, producing inflated, compound lava flows similar to those seen at Kilauea in Hawaii. Images from the Galileo spacecraft revealed that many of Io's major lava flows, like those at Prometheus and Amirani , are produced by the build-up of small breakouts of lava flows on top of older flows. Analysis of the Voyager images led scientists to believe that these flows were composed mostly of various compounds of molten sulfur. Terrestrial Heat Flow in New Zealand However, subsequent Earth-based infrared studies and measurements from the Galileo spacecraft indicate that these flows are composed of basaltic lava with mafic to ultramafic compositions. The discovery of plumes at the volcanoes Pele and Loki were the first sign that Io is geologically active. Additional material that might be found in these volcanic plumes include sodium, potassium , and chlorine. Examples of this plume type include Pele, Tvashtar, and Dazhbog. Another type of plume is produced when encroaching lava flows vaporize underlying sulfur dioxide frost, sending the sulfur skyward. This type of plume often forms bright circular deposits consisting of sulfur dioxide. Examples include Prometheus, Amirani, and Masubi. The erupted sulfurous compounds are concentrated in the upper crust from a decrease in sulfur solubility at greater depths in Io's lithosphere and can be a determinant for the eruption style of a hot spot. Io has to mountains. Despite the extensive volcanism that gives Io its distinctive appearance, nearly all its mountains are tectonic structures, and are not produced by volcanoes. Instead, most Ionian mountains form as the result of compressive stresses on the base of the lithosphere, which uplift and often tilt chunks of Io's crust through thrust faulting. Mountains on Io generally, structures rising above the surrounding plains have a variety of morphologies. Plateaus are most common. Other mountains appear to be tilted crustal blocks, with a shallow slope from the formerly flat surface and a steep slope consisting of formerly sub-surface materials uplifted by compressive stresses. Both types of mountains often have steep scarps along one or more margins. Only a handful of mountains on Io appear to have a volcanic origin. Other shield volcanoes with much shallower slopes are inferred from the morphology of several of Io's volcanoes, where thin flows radiate out from a central patera, such as at Ra Patera. Nearly all mountains appear to be in some stage of degradation. Large landslide deposits are common at the base of Ionian mountains, suggesting that mass wasting is the primary form of degradation. Scalloped margins are common among Io's mesas and plateaus, the result of sulfur dioxide sapping from Io's crust, producing zones of weakness along mountain margins. Terrestrial Heat Flow through Salt-Marsh Peat. Io has an extremely thin atmosphere consisting mainly of sulfur dioxide SO 2 , with minor constituents including sulfur monoxide SO , sodium chloride NaCl , and atomic sulfur and oxygen. The maximum atmospheric pressure on Io ranges from 3. The thin atmosphere also necessitates a rugged lander capable of enduring the strong Jovian radiation , which a thicker atmosphere would attenuate. Gas in Io's atmosphere is stripped by Jupiter's magnetosphere, escaping to either the neutral cloud that surrounds Io, or the Io plasma torus, a ring of ionized particles that shares Io's orbit but co-rotates with the magnetosphere of Jupiter. The collapse during eclipse is limited somewhat by the formation of a diffusion layer of sulfur monoxide in the lowest portion of the atmosphere, but the atmosphere pressure of Io's nightside atmosphere is two to four orders of magnitude less than at its peak just past noon. Various researchers have proposed that the atmosphere of Io freezes onto the surface when it passes into the shadow of Jupiter. Evidence for this is a "post-eclipse brightening", where the moon sometimes appears a bit brighter as if covered with frost immediately after eclipse. After about 15 minutes the brightness returns to normal, presumably because the frost has disappeared through sublimation. High-resolution images of Io acquired when Io is experiencing an eclipse reveal an aurora -like glow. Aurorae usually occur near the magnetic poles of planets, but Io's are brightest near its equator. Io lacks an intrinsic magnetic field of its own; therefore, electrons traveling along Jupiter's magnetic field near Io directly impact Io's atmosphere. More electrons collide with its atmosphere, producing the brightest aurora, where the field lines are tangent to Io i. Aurorae associated with these tangent points on Io are observed to rock with the changing orientation of Jupiter's tilted magnetic dipole. Media related to Io at Wikimedia Commons. From Wikipedia, the free encyclopedia. For other uses, see Jupiter 1. Innermost of the four Galilean moons of Jupiter. Galileo spacecraft true-color image of Io. The dark spot just left of the center is the erupting volcano Prometheus. The whitish plains on either side of it are coated with volcanically deposited sulfur dioxide frost, whereas the yellower regions contain a higher proportion of sulfur. Alternative names. Mean orbit radius. Orbital period. Average orbital speed. Surface area. Mean density. Surface gravity. Moment of inertia factor. This item appears in the following Collection(s) Rotation period. Apparent magnitude. Surface pressure. Main article: Exploration of Io. Io's Laplace resonance with Europa and Ganymede click for animation. See also: Tidal heating. Main article: Tidal heating of Io. Play media. Main article: Volcanology of Io.

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— OR — Using Doubles Addition Activity, students solve doubles fact addition problems by matching equations and sums. Knowing your doubles facts helps your students improve their mental math strategies. This activity will give your students the opportunity to practice. Students match addition equations to their sums. If you are using this activity, your students are probably learning about addition! Use this Single Digit Addition Activity as an additional resource for your students. Introduce this activity by reviewing addition facts using the Addition Flash Cards.Then, have students complete activity independently or with a partner. Finally, studentscheck over your answers with a partner and fix any incorrect answers. Once finished, have students write their own word problem based on the equations from the activity. Finally, Students can continue their practice with this Adding Doubles Worksheet. Be sure to check out more Addition Activities. Tell others why you love this resource and how you will use it. You must be logged in to post a review. Make Resources FREE with a Membership!

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The ongoing Lunar Laser Ranging experiment or Apollo landing mirror measures the distance between surfaces of Earth and the Moon using laser ranging. Lasers at observatories on Earth are aimed at retroreflectors planted on the Moon during the Apollo program (11, 14, and 15), and the two Lunokhod missions. Laser light pulses are transmitted and reflected back to Earth, and the round-trip duration is measured. The lunar distance is calculated from this value. The first successful tests were carried out in 1962 when a team from the Massachusetts Institute of Technology succeeded in observing laser pulses reflected from the Moon's surface using a laser with a millisecond pulse length. Similar measurements were obtained later the same year by a Soviet team at the Crimean Astrophysical Observatory using a Q-switched ruby laser. Greater accuracy was achieved following the installation of a retroreflector array on July 21, 1969, by the crew of Apollo 11, and two more retroreflector arrays left by the Apollo 14 and Apollo 15 missions have also contributed to the experiment. Successful lunar laser range measurements to the retroreflectors were first reported[when?] by the 3.1 m telescope at Lick Observatory, Air Force Cambridge Research Laboratories Lunar Ranging Observatory in Arizona, the Pic du Midi Observatory in France, the Tokyo Astronomical Observatory, and McDonald Observatory in Texas. The uncrewed Soviet Lunokhod 1 and Lunokhod 2 rovers carried smaller arrays. Reflected signals were initially received from Lunokhod 1, but no return signals were detected after 1971 until a team from University of California rediscovered the array in April 2010 using images from NASA's Lunar Reconnaissance Orbiter. Lunokhod 2's array continues to return signals to Earth. The Lunokhod arrays suffer from decreased performance in direct sunlight—a factor considered in reflector placement during the Apollo missions. The Apollo 15 array is three times the size of the arrays left by the two earlier Apollo missions. Its size made it the target of three-quarters of the sample measurements taken in the first 25 years of the experiment. Improvements in technology since then have resulted in greater use of the smaller arrays, by sites such as the Côte d'Azur Observatory in Nice, France; and the Apache Point Observatory Lunar Laser-ranging Operation (APOLLO) at the Apache Point Observatory in New Mexico. The distance to the Moon is calculated approximately using the equation: distance = (speed of light × duration of delay due to reflection) / 2 To compute the lunar distance precisely, many factors must be considered in addition to the round-trip time of about 2.5 seconds. These factors include the location of the Moon in the sky, the relative motion of Earth and the Moon, Earth's rotation, lunar libration, polar motion, weather, speed of light in various parts of air, propagation delay through Earth's atmosphere, the location of the observing station and its motion due to crustal motion and tides, and relativistic effects. The distance continually changes for a number of reasons, but averages 385,000.6 km (239,228.3 mi) between the center of the Earth and the center of the Moon. At the Moon's surface, the beam is about 6.5 kilometers (4.0 mi) wide[i] and scientists liken the task of aiming the beam to using a rifle to hit a moving dime 3 kilometers (1.9 mi) away. The reflected light is too weak to see with the human eye. Out of 1017 photons aimed at the reflector, only one is received back on Earth, even under good conditions. They can be identified as originating from the laser because the laser is highly monochromatic. This is one of the most precise distance measurements ever made, and is equivalent in accuracy to determining the distance between Los Angeles and New York to within 0.25 mm (0.01 in). The upcoming MoonLIGHT reflector, that may be placed during an attempt by the private MX-1E lander, is designed to increase measurement accuracy 100 times over existing systems. MX-1E was set for launch in July 2020, however, as of February 2020, the launch of the MX-1E has been canceled. Apollo 14 Lunar Ranging Retro Reflector (LRRR) APOLLO Collaboration photon pulse return times Laser Ranging at Goddard Space Flight Center

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How to write a story middle ks2 What are they dressed like? Packed with entertaining illustrations that will inspire new writer, this book is filled with tips on how to write in particular genres, create exciting characters, and write powerful sentences using metaphors, similes, and idioms. Why Use This Tip Writing stories is something every child is asked to do in school, and many children write stories in their free time, too. For students to improve their writing craft, it is important they know when to switch from story-telling mode to story-showing mode. Good luck! Notes This activity may take up to 1 hour 10 minutes. Story plan example ks2 Keep this book on the shelf with other stories and encourage the child to read it to you. A limp? Or you could move from page to screen and get coding to create an animated tale. By familiarizing a child with how authors create stories and what the different parts of a story are, introducing visual or written prompts that inspire him or her to think of story ideas, and encouraging him or her to plan before starting to write, you'll help the child make a complete and imaginative story. Does the event change how the characters act or speak or how they feel? Teach your students to write creative narratives and stories through proven methods of character creation, plot development, researching and writing skills. Think about the books you are reading. For students to improve their writing craft, it is important they know when to switch from story-telling mode to story-showing mode. Take on board their feedback as constructive advice. A photo story is another way of using pictures to organize or create a story. Story writing ks2 worksheets If so, how does it get resolved? If something had been stolen, what would they do? What do they do? Teach your students to write creative narratives and stories through proven methods of character creation, plot development, researching and writing skills. Help the child understand that the author created or adapted the story and made decisions about what should happen in it. They work kind of like a comic strip. You can conquer this fear by finding an opening line. Where are they from? A writer's notebook is a private place where you can gather your inspiration. A visit to an art gallery or even just looking at photos in a magazine can inspire a story. Making a map If you are a big fantasy fan and love stories about dragons, wizards and monsters, try to create your own magical land. Or is it an overcrowded 16th century London with human waste stinking up the streets. Hurdles are not always successfully overcome. It might be a small relayed detail in the way they walk that reveals a core characteristic. A character who sits down at the family dinner table and immediately snatches up his fork and starts stuffing roast potatoes into his mouth before anyone else has even managed to sit down has revealed a tendency towards greed or gluttony. based on 49 review

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Before the lesson - To explore stereotypes in fictional characters and think about how these might influence us Pupils should be taught: - What a stereotype is, and how stereotypes can be unfair, negative or destructive Pupils needing extra support: May need help with understanding what a A generalised or over-simplified image or idea of a particular type of person or thing that is often untrue…. is and could benefit from books to help them with the activity. Pupils working at greater depth: Can be challenged to consider if there are differences between characters from traditional stories and older books and more modern stories – have stereotypes lessened over time?

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Search Within Results Common Core: Standard Common Core: ELA Common Core: Math - Student Outcomes Students understand how a formula for the nth roots of a complex number is related to powers of a complex number. Students calculate the nth roots of a complex number. - Student Outcomes Students interpret complex multiplication as the corresponding function of two real variables. Students calculate the amount of rotation and the scale factor of dilation in a... - Student Outcomes Students create a sequence of transformations that produce the geometric effect of reflection across a given line through the origin. - Student Outcomes Students derive the formula for zn = rn(cos(nθ) + i sin(nθ)) and use it to calculate powers of a complex number. - Topic C highlights the effectiveness of changing notations and the power provided by certain notations such as matrices. The study of vectors and matrices is introduced through a coherent connection... - Precalculus Module 1: Complex Numbers and Transformations Module 1 sets the stage for expanding students' understanding of transformations by exploring the notion of linearity. This leads to the...

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Presentation on theme: "Starter Open “Quiz” from the Department Share or VLE See if you can unscramble the letters to get the keywords for today's lesson…"— Presentation transcript: Starter Open “Quiz” from the Department Share or VLE See if you can unscramble the letters to get the keywords for today's lesson… Lesson Objectives By the end of the lesson you will be able to: 1.Identify different data types 2.Select appropriate data types for a given set of data Data… What is data? In 10 words or less, write down what you understand data to be… Data… Data is raw facts and figures. Data on it’s own has no meaning. Some examples: a3z B2.2 d2d4 wig Data Types Data comes in many different forms. It could be all stored in the same way but it wouldn’t be very useful. This is why we have Data Types. Task 1 Open the “What are Data Types” PowerPoint from the shared area. Read it… Task 2 Either create a mind map / spider diagram or traditional plain old notes in your book about each data type. You must include the name of the data type, a description and an example. Extension: find out WHY each data type is needed. Task 3 Complete the worksheet you have been given. This will be completed for homework if you don’t finish it during the lesson. Stick the worksheet in your book. Plenary Without looking in your book… Explain to the person sitting next to you what a data type is… Then swap over so the other person can explain two reasons why selecting the correct data type is important. Write your answers down in your book.

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Geological Environment and Processes Responsible 4 Geological and Topographical Features of the Plate Margin 6 Human and Environmental Impacts 8 On 11 April 2012 two huge earthquakes occurred beneath the floor of the Indian Ocean, off the coast of North Sumatra. Registering a magnitude of 8.6, the first was followed by another of 8.2 magnitude, which scientists subsequently identified as an aftershock. Neither triggered a large scale tsunami, which scientists attribute to the movement being of the “strike-slip” type, rather than the “thrust” type. However, strike-slip earthquakes are normally of a much lesser magnitude. This one caused a relative lateral shift of part of the ocean floor of around 70 feet, compared with the previously largest recorded strike-slip earthquake, which was in San Francisco in 1906, and where the lateral movement was just 15 feet. Further, the location of this April’s earthquake was unusual – approximately 100 km from the boundary between the Indo-Australia plate and the Sunda plate (Bradbury, Apr. 2012). The Figure below shows the earthquake’s epicentre location (star shape) and the boundaries of the various major and minor tectonic plates in the vicinity. Figure 1: Location of the April 2012 Earthquake (Extracted from: “Indonesian Quake Rattles Island Nation.” Real Science.) This essay seeks to explain why many believe that the earthquake on April 11 2012 was part of “the difficult process of breaking a tectonic plate” (Barras, Sep. 2012). According to Barras the aftershocks were felt “the world over” and “provided the best evidence yet that the vast Indo-Australian plate is being torn in two.” Geological Environment and Processes Responsible Barras reports that geologists have been seeking to determine why the earthquake occurred where it did – away from a plate boundary – and was of the strike-slip type, in which the rocks either side of the fault grind past each other in a lateral direction, as opposed to the more usual earthquakes at plate boundaries, in which one part of the Earth’s crust slides beneath another (a process known as subduction). Those are either “normal” or “thrust” types. In the latter case, the displaced rock moves upwards, which is what causes a tsunami when the location is beneath an ocean. The Figure below illustrates the movements involved in those three types of earthquake. Figure 2: Types of Movements in Earthquakes (Extracted from: “Indonesian Quake Rattles Island Nation.”) Barras refers to research by French scientists on earthquakes in the area, which found that 26 of those earthquakes between December 2004 and April 2011 were of the strike-slip type, which they believe suggests that “the Indo-Australian plate is breaking up along a new plate boundary.” Further, those scientists suggest that even though India and Australia are located over the same tectonic plate, Australia’s movement is actually faster than that of India. The effect of that movement rate differential is to cause a central area of the Indo-Australian plate to begin to buckle, which may in turn be causing the plate to split. In more detail, though on a wider scale, the movement of the Indo-Australian plate is in a northerly direction, but its western half is being impeded by the Himalayas. That uneven pressure causes an area of compression in the plate’s central area, which as a consequence may be causing the plate to crack. In the following Figure illustrating the process, the vertical dotted line represents the possible new plate boundary. Figure 3: Uneven Indo-Australian Plate Movement (Extracted from: “Earth cracking up under Indian Ocean.”) Although not everyone supports the views of those French scientists, Meng – at the University of California in Berkeley – believes that they may be right. He says: “I think it's a fair argument that the 11 April earthquakes may mark the birth of a plate boundary.” A researcher at the US Geological Survey reported that he and his colleagues had observed that in the six days following the 11 April earthquake there were almost five times as many earthquakes around the world than normal – a phenomenon never previously seen (Barras). More details of what seismologists believe actually occurred on April 11 2012 are provided in an ABC Science article entitled “Quake start of Indo-Australia plate split” (27 Sep. 2012). They believe there was what they call “A near simultaneous rupturing of at least four faults, stacked up and lying at right angles to one another.” Data suggests they opened one at a time, but all within a space of less than three minutes. As mentioned by others, they also note that it occurred well away from known plate boundaries, tearing a wide gash in the plate, “confirming long-held suspicions that the plate is fragmenting.” Geological and Topographical Features of the Plate Margin The boundary or margin of the Indo-Australian plate in the area of Sumatra (the area nearest to where the stresses are believed to be associated with the breakup of the plate) is a subduction type boundary; i.e. where the oceanic plate descends beneath the Eurasian or Sunda plate, as shown in the Figure (“Subduction zone beneath Sumatra, Indonesia”): Figure 4: Indo-Australian Plate Boundary: Sumatra (Extracted from: “Subduction zone beneath Sumatra, Indonesia”). As explained in the article, when the subducted Indo-Australian plate descends beyond 100km, the water within it lowers the melting point of the rock, creating magma, which – because it is hotter and less dense – migrates to the surface, generating the volcanic activity typical of Sumatra. The volcanoes there are in a chain running generally circa 300km away from a deep oceanic trench, which effectively forms the boundary between the two tectonic plates in this area. Overall, the northern boundary of the Australian part of the Indo-Australian plate is complex in tectonic terms (Blewett, Kennett & Huston, 2012). In the area of New Guinea, the Australian and Pacific Plates are colliding, but further west the interaction is with the Eurasian Plate. In that section of the boundary, the boundary type is that of collision in the region known as the Banda Arc, changing to subduction in the area of the Java and Sumatra trenches (Indonesia). The following Figure illustrates those boundaries (circled): Figure 5: Australian Plate Boundaries (Extracted from: “Shaping a Nation: A Geology of Australia.”) As noted by Blewett et al., the eastern and northern boundaries of the Australian Plate are part of the so-called “Pacific Rim of Fire” – a region of the world which experiences a third of all the world’s earthquakes, and is the location of three quarters of the world’s volcanoes. Human and Environmental Impacts When the build up of stresses – usually at plate boundaries – cause earthquakes of the types that in turn trigger tsunamis, the immediate human impact can tragically be a considerable loss of lives. For example, a tsunami associated with a 7.7 magnitude earthquake just off Sumatra in 2010 caused the loss of over 100 lives, while a volcanic eruption on Java, about 800 miles east, caused the deaths of more than 20 people (Belford, Oct. 2010). The same New York Times article notes that a 9.1 magnitude earthquake centred on the same geological fault in 2004 triggered a tsunami that killed a massive 230,000 or more people in the area of the Indian Ocean, with northern Sumatra being the worst hit. There are two main factors that might mitigate the human impact in terms of loss of lives, in the event of future earthquakes associated with the breakup of the Indo-Australian Plate. Firstly, that if future earthquakes are also of the strike-slip variety (as was the April 2012 seismic event), it is possible that there will not be associated major tsunamis. Secondly, if they occur in a similar area, i.e. at some distance from the plate boundary and away from land, the likelihood of collateral damage is reduced. There is of course no guarantee that they always will happen a long way from inhabited land masses, but the location of the suspected deformation and buckling of the Indo-Australian Plate makes that more likely. Taking a more pessimistic view, Sharwood (27 Sep. 2012) reminds us that – notwithstanding the ultimate plate breakup will occur at a very long time in the Earth’s geological future, there are 127 active volcanoes and 300 million people in Indonesia. In certain circumstances and at any time in the future, the human impact could be enormous. An important factor affecting the degree of human impact of earthquakes is the global population growth coupled with increasing urbanization (often of poor quality construction) in earthquake-prone regions. This has been particularly so in recent history in the area of the Pacific Rim, where over 80 percent of the world’s earthquakes have occurred (Doocy, Daniels, Packer, Dick and Kirsch, Apr. 2013). As their Public Library of Science article states, “The primary cause of earthquake-related mortality was building collapse, most frequently leading to soft tissue injuries, fractures and crush injuries/syndrome.” As far as environmental impact in the immediate future is concerned, it is reasonable to take a pragmatic view; i.e. that earthquakes occurring as part of the progressive plate breakup and centred well away from the land, hence not triggering a tsunami, are likely to have little effect on the environment, unless they in turn trigger other earthquakes or seismic events such as volcanic eruptions, for example. In the longer term, due to the ongoing breakup of the plate – which experts believe has already been happening for around 15 million years (Spinks, Mar. 2013) – there will doubtless be many, many more earthquakes, as India and Australia move in approximately the same north to north-easterly direction, but with Australia moving faster than India. The Spinks article suggests that “Over the next few tens of thousands of years” the most affected area southwest of Northern Sumatra is likely to suffer more earthquakes, but there could also be more earthquakes within continental Australia, even though it is thousands of kilometres distant from the area directly affected. The article further suggests that the breakup process has already created a new tectonic plate, known as the Capricorn Plate, although its existence is not yet proven. (Note: The Capricorn Plate location is depicted in the previous Figure). In addition to tsunamis, other environmental impacts of earthquakes mentioned in the Spinks article include landslides, which can occur in hilly terrain, due the vibrations from earthquakes. Dependent on the precise locations, such landslides can of course cause loss of life and/or damage to property. Reassuringly, the article suggests there is little chance of the Australian mainland splitting in two. In contrast, it is evident from local earthquakes within the Australian continental landmass that Australia is instead subject to horizontal compression, squeezing opposite sides of faults together. That is likely to cause an uplift of the principal earthquake areas. It interesting to note that a considerable amount of the media coverage of the April 11 2012 earthquake implies that it was the “beginning” of the process of the Indo-Australian Plate breaking up; yet other comment – sometimes in the same article – also notes that the process could have been in action for a very long time. One article suggests it has been happening for 15 million years so far, and is likely to continue for a similarly vast amount of time in the future. In fact, according to Dr Christopher Scotese, a geologist at the University of Texas, it is possible that in 250 million years time the ever-continuing drift of the world’s tectonic plates will have resulted in the great majority of the Earth’s landmasses merging into a single “super-continent” which he calls “Pangea Ultima” (Scotese, last updated Apr. 2011). He admits that most of such prediction up to around 50 million years into the future is based on the continuation of current plate movements, but that beyond 50 million years guesswork plays a major part. Whilst appreciation of these enormous timescales puts the process into a more realistic long-term perspective, it in no way diminishes the need to maintain short-term concern about the potential dangers from future earthquakes, volcanic eruptions and tsunamis. However, as far as the latter phenomenon is concerned, there are now increasingly efficient tsunami warning networks in place. These facilitate the issuing of a limited amount of early warning of the arrival of one of these rapidly-moving travelling waves that can cause severe damage and loss of life. The “Australian Tsunami Warning System” (2014) describes the system that is available to provide Australian populations with between two and four hours warning, and which forms an integral part of the Indian Ocean Tsunami Warning and Mitigation System. From consideration of scientific opinion on the subject, it seems reasonable to expect that earthquakes associated with plate breakup are more likely to be of the strike-slip variety, and therefore less likely to trigger tsunamis. However, as was demonstrated by the April 11 2012 event, they can cause seismic disturbances including other earthquakes in locations at great distances from the initial event, so can still be a significant hazard. According to Spinks (2013) the elastic seismic waves initiated when an earthquake occurs travel at a great speed (between 4 and 10 kilometres per second), meaning that they could reach the opposite side of the planet (about 13,000 kilometres) in less than 20 minutes. There is little doubt that the Indo-Australian Plate is being subjected to uneven forces and stresses that may eventually cause it to split completely, and which almost certainly have already caused the creation of a new tectonic plate called the Capricorn Plate. Whilst those stresses have caused earthquakes, most notably on April 11 2012, a positive factor is that because they appear to be occurring well away from the northern boundary of the plate and therefore at some distance from inhabited landmasses, the human impact is not as severe as it might have otherwise been. Added to that, because the April 11 2012 earthquake was of the strike-slip type, there was no associated tsunami, further mitigating potential human and environmental impacts. It is to be hoped that future seismic events associated with the continuation of this tectonic drift process will be of a similar nature; i.e. will not result in either serious losses of lives or major environmental damage. Regrettably, because earthquake prediction is by no means an exact science, only time will tell. “Australian Tsunami Warning System.” (2014). Australian Government Bureau of Meteorology. Available at: http://www.bom.gov.au/tsunami/about/atws.shtml Barras, Colin. (26 Sep. 2012). “Earth cracking up under Indian Ocean.” New Scientist, Issue 2884. Available at: http://www.newscientist.com/article/mg21528843.500-earth-cracking-up-under-indian-ocean.html#.Uv3hILeYY3x Belford, Aubrey. (26 Oct. 2010). “Tsunami and Volcano Batter Indonesia.” The New York Times. Available at: http://www.nytimes.com/2010/10/27/world/asia/27indo.html Blewett, Richard, S., Kennett, Brian, L., N., & Huston, David, L. (2012). “Shaping a Nation: A Geology of Australia.” Research School of Earth Sciences: Australia National University. Available at: http://rses.anu.edu.au/~brian/PDF-reprints/2012/SN-chapter-2.pdf Bradbury, Michael. (11 Apr. 202). “Indonesian Quake Rattles Island Nation.” Real Science. Available at: http://www.realscience.us/2012/04/11/indonesian-quake-rattles-island-nation/ Doocy, Shannon, Daniels, Amy, Packer, Catherine, Dick, Anna, and Kirsch, Thomas, D. (Apr. 2013). “The Human Impact of Earthquakes: a Historical Review of Events 1980-2009 and Systematic Literature Review.” Public Library of Science, PLoS Curr. 2013 April 16; 5: ecurrents.dis.67bd14fe457f1db0b5433a8ee20fb833. Available at: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3644288/ “Quake start of Indo-Australia plate split.” (27 Sep. 2012). ABC Science. Available at: http://www.abc.net.au/science/articles/2012/09/27/3599041.htm Scotese, Dr. Christopher. (Last updated Apr. 2011). “Continents in Collision: Pangea Ultima.” NASA Science News. Available at: http://science1.nasa.gov/science-news/science-at-nasa/2000/ast06oct_1/ Sharwood, Simon. (27 Sep. 2012). “Mighty quake shook ENTIRE PLANET, broke tectonic plate.” The Register. Available at: http://www.theregister.co.uk/2012/09/27/earthquake_broke_tectonic_plate/ Spinks, Peter. (Mar. 2013). An earth-shattering break-up.” The Sydney Morning Herald. Available at: http://www.smh.com.au/environment/an-earthshattering-breakup-20130320-2gfib.html “Subduction zone beneath Sumatra, Indonesia.” (n.d.). Earth Observatory of Singapore. Available at: http://www.earthobservatory.sg/resources/images/subduction-zone-under-sumatra-indonesia#.Uv4nereYY3x

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ESL lesson plans provide a structured breakdown of what you intend to do during class time. They require careful planning in advance and ensure that each lesson you teach has a purpose and advances the overall curriculum and class goals. How do you format a lesson plan? Identify the objectives. Determine the needs of your students. Plan your resources and materials. Engage your students. Instruct and present information. Allow time for student practice. Ending the lesson. Evaluate the lesson. How do you write a PPP lesson plan? How do you present a lesson? What do you teach in ESL? Teachers who know how to teach an ESL class may use strategies and assignments such as: What should an ESL curriculum include? As a rule, ESL English lessons for students from beginner to intermediate levels should focus on all language skills – reading, writing, speaking, and listening. It is important to incorporate these four parts in your lessons and devote an equal amount of time to each of them. via How do you structure a lesson? What makes a good PPP lesson? Excellent presentation techniques: Ask questions that will help them understand the new material and try not to tell them answers, allowing them to work it out with an English thinking mind. Use visuals to stimulate understanding and to get your students enthused about a topic. via What is PPP teaching method? PPP is a paradigm or model used to describe typical stages of a presentation of new language. It means presentation, production and practice. The practice stage aims to provide opportunities for learners to use the target structure. Then learners use prompts to complete sentences with the correct forms of the verbs. via What is a PPP lesson plan? Presentation, practice and production (PPP) A deductive approach often fits into a lesson structure known as PPP (Presentation, Practice, Production). The teacher presents the target language and then gives students the opportunity to practise it through very controlled activities. via What are the 4 A's in lesson plan? Choose a topic that you want the children in your class to learn and apply the 4-A's of activating prior knowledge, acquiring new knowledge, applying the knowledge, and assessing the knowledge. via What are the 7 E's of lesson plan? The 7 Es stand for the following. Elicit, Engage, Explore,Explain, Elaborate, Extend and Evaluate. via What is a 5 step lesson plan? The five steps involved are the Anticipatory Set, Introduction of New Material, Guided Practice, Independent Practice and Closure. via What are the 6 components of a lesson plan? The most effective lesson plans have six key parts: What are the components of ESL? English Language Learners and the Five Essential Components of Reading Instruction What ESL curriculum pedagogies do you implement in the classroom? All Answers (8) How do you start and end a lesson? How do you motivate students before a lesson? What are the seven ways in presenting the lesson effectively? 7 Presentation Tips for Teachers Images for Esl Lesson Plan Template Write daily lesson plan template Lesson plan template worksheet free esl printable Lesson plan template blank high school Esl lesson plan template Customize lesson plan templates online Esl reading lesson plan template Stem lesson plan template inspirational simple grade Lesson plan model esl worksheet Esl lesson plan free lessons templates Framework lesson plan template luxury Lesson plan sample free Weekly learning plan lesson templates esl A focus on student talking time: A good English language lesson allows for about 80% student talking time. You should be exhausted at the end of each lesson! 4. A clear link between the lesson and everyday life: Your lesson must be centered on everyday situations in your workplace and in your community.

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When a ray is drawn from the origin of the unit circle, it will intersect the unit circle at a point (x, y) and form a right triangle with the x-axis, as shown above. The hypotenuse of the right triangle is equal to the radius of the unit circle, so it will always be 1. Based on the Pythagorean Theorem, the equation of the unit circle is therefore: x2 + y2 = 1 Unit circle definitions of trigonometric functions The unit circle is often used in the definition of trigonometric functions. Below is a figure showing all of the trigonometric relationships as they relate to the unit circle. In the figure above, point A has coordinates of (x, y). Together with θ, the angle formed between the initial side of an angle along the positive x-axis and the terminal side of the angle formed by rotating the ray counter-clockwise, we can form a right triangle. Using the fact that the radius of the unit circle is 1 (and therefore the hypotenuse of the right triangle is equal to 1), we can use the right triangle definitions of the trigonometric functions to find that , and . Based on this, we can determine the definitions of the rest of the trigonometric functions, as shown in the table below. Commonly used angles While we can find trigonometric values for any angle, some angles are worth remembering because of how frequently they are used in trigonometry. The angles are 30°, 45° and, 60°. In radians, they correspond to respectively. Below is a table of the values of these angles, as well as a figure of the values on a unit circle. As can be seen from the table or the unit circle above, there are three values to remember: . Because of the nature of the unit circle, these values are the same for their respective angles in different quadrants on the unit circle, with the only difference being their signs based on the quadrant the angle is in. Therefore, remembering these three values and how they correspond to multiples of 30°, 45° and 60° will enable you to fill in all the values on the unit circle. The other angles on the unit circle to remember are those whose terminal sides lie on the x- or y-axis: 0° or 0 (which has equivalent sine and cosine values as 360° or 2π), 90° or , 180° or π and, 270° or . At any of these angles, sin(θ) or cos(θ) has a value of –1, 0, or 1. |180° or π||0||-1||0| Method for memorizing common values One method that may help with memorizing the common trigonometric values is to express all the values of sin(θ) as fractions involving a square root. Starting from 0° and progressing through 90°, sin(0°) = 0 = . The subsequent values, sin(30°), sin(45°), sin(60°), and sin(90°) follow a pattern such that, using the value of sin(0°) as a reference, to find the values of sine for the subsequent angles, we simply increase the number under the radical sign in the numerator by 1, as shown below. The values of sine from 0° through -90° follows the same pattern except that the values are negative instead of positive since sine is negative in quadrant IV. This pattern repeats periodically for the respective angle measurements, and we can identify the values of sin(θ) based on the position of θ in the unit circle, taking the sign of sine into consideration: sine is positive in quadrants I and II and negative in quadrants III and IV. A similar memorization method can be used for cosine. Starting from 0° and progressing through 90°, cos(0°)=1=. The subsequent values, cos(30°), cos(45°), cos(60°), and cos(90°) follow a pattern such that, using the value of cos(0°) as a reference, to find the values of cosine for the subsequent angles, we simply decrease the number under the radical sign in the numerator by 1, as shown below: From 90° to 180°, we increase the number under the radical by 1 instead, but also must take into account the quadrant that the angle is in. Cosine is negative in quadrants II and III, so the values will be equal but negative. In quadrants I and IV, the values will be positive. This pattern repeats periodically for the respective angle measurements. As long as we remember these values, it is possible to use the relationship

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A fraction is part of a whole and is shown by writing one whole number above another. It can also be shown by a diagram. Fractions are equivalent if they are of equal value. Equivalent fractions can have different numerators and denominators. Simplified fractions have no common factors other than 1. There are different types of fractions - a fraction can be proper, improper or a mixed number. It can be useful to order a group of numbers by their value. Fractions can be arranged in ascending or descending order. Learn how to order fractions. Learn how to add fractions, including those with the same denominators and different denominators. Learn how to subtract fractions, including those with the same denominators and different denominators. Learn how to multiply fractions as well as multiply mixed numbers. Divide a fraction using the reciprocal method by turning the second fraction upside down and multiplying. Learn how to find a fraction of an amount. Learn how to find an amount from a given fraction. Learn how to convert between fractions and decimals using equivalent fractions or division. Fractions expressed as percentages can be easier to interpret. Learn how to convert fractions to percentages. Calculations often give a decimal answer. Converting a decimal to a percentage as a percentage is often easier to understand. Learn how to convert decimals to percentages. Percentages are always out of 100. This is important to remember when converting percentages to fractions and decimals. We have a selection of great videos for use in the classroom

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Students will be able to apply the breaking apart strategy to solve multiplication problems involving up to four-digit numbers. Students will be able to use their understanding of place value when breaking apart a larger multiplication problem and putting the answers together to find a solution. Tell your students that they will need to apply their understanding of place value throughout today's lesson. Spend a few minutes reviewing place value before getting into the actual lesson. Great examples of questions you could ask are: What is place value? How is understanding place value helpful when completing math problems? Write a two-digit number on the board, such as 64. Ask your students how they could break this number down by place value or expanded notation. Remind students that expanded notation means writing a number to show the value of each digit. Write the two-digit number in expanded form. For example: 64 = 60 + 4. Make sure your students understand that these numbers came from identifying the total of tens and ones in the number. Do this same process for a few more increasingly larger numbers, such as: 79, 234, 1456.

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Solving Equations Worksheets Tips for solving equations An equation can be hard to understand. Ranging from a single equation to a multi-step equation, mathematics has a variety of them. The only way to crack single, multi-step, and complex equations is to learn the tips and hacks to solve them skillfully. All equations, either single or multi-step, have an equal sign. Follow the below mentioned tricks and methods to solve equations. 1. Ensure that the equations maintain a balance with the equality sign in between, making it equal at both hands. 2. Isolate the variables on one side of the equation. 3. Look for any fractions in the equations. If you find any, make sure to convert them into decimals or remove them altogether. 4. Look for parenthesis and solve them first in the equation. 5. Make sure that the variable terms are on one side, and the constants, if any, are on the other side. 6. Undo the already done operations in the equation. 7. Take the constants on the other side and simplify. Demonstrates how to simplify and reorder variables within an equation. Practice problems are provided.View worksheet Explains how to reorder and require terms while solving equations. Practice problems are provided. Example: Simplify: 5x = 25. Solving for variable x requires dividing 25 by 5: x = 25 / 5. Solve: x = 5.View worksheet Independent Practice 1 Contains 20 solving equations problems. The answers can be found below.View worksheet Independent Practice 2 Features another 20 solving equations problems.View worksheet 12 solving equations problems for students to work on at home. Example problems are provided and explained.View worksheet 10 solving equations problems. A math scoring matrix is included.View worksheet Homework and Quiz Answer Key Answers for the homework and quiz.View worksheet Lesson and Practice Answer Key Answers for both lessons and both practice sheets.View worksheet What's an Equation? An equation states that two numbers or expressions are equal. Equations are useful for relating variables and numbers. Word problems are written down as equations to weed out unnecessary information. There are rules for simplifying equations.

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Commutative, Associative, and Distributive Properties Worksheets What are Commutative, Associative, Distributive Properties? Commutative, associative, and distributive properties are the three properties underpinning the fundamentals of algebra. Students are first introduced with these properties in broader terms in the early years. However, as the students learn advance concepts, the understanding of these properties become essential. Commutative Property - Commutative is derived from the word commute, which means to move around. As the name implies, the commutative property refers to moving the numbers around. The commutative rule states that if we move the numbers around, we will still get the same answer. The equation of commutative property of addition is written as: a + b = b + a. The equation of commutative property of multiplication is written as: a x b = b x a. Associative Property - The word associative is derived from the word 'associate' which means to 'group'. And as the name implies, associative property refers to associating or grouping number. The associative property also states that grouping and regrouping of numbers don't affect the result. The equation of associative property of addition is written as: (a + b) + c = a + (b + c) The equation of associative property of multiplication is written as: a x (b x c) = (a x b) x c Distributive Property - Distributive property states that multiplication distributes over addition. The equation of this property is written as: a x (b + c) = a x b + a x c. Reviews each property and provides examples. Demonstrates the identification of properties. Identify which property is used in each computation.View worksheet Independent Practice 1 Complete problems like: Addends can be added in any order without changing the sum. This is _________________ property. The answers can be found below.View worksheet Independent Practice 2 This property says multiplying a sum by some number is the same as multiplying each term by that same number. What is it?View worksheet 8 property questions for students to work on at home. Examples of each property are provided and explained.View worksheet 10 read skill property problems. A math scoring matrix is included.View worksheet Homework and Quiz Answer Key Answers for the homework and quiz.View worksheet Lesson and Practice Answer Key Answers for both lessons and both practice sheets.View worksheet The commuting distance is the same in either direction, from home to work or work to home. Associative Property- To associate with people is to group with them. Distributive Property- To distribute something is to give it to everyone.

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Strategy 3: Implement comprehension strategies before reading What to Do - Activate background knowledge by previewing literacy materials - Exploring objects in story bag/box - Picture walk - teacher walks and talks the child through the pages to point out key features of the images on the pages or the objects added to the pages or tactile cues and print/braille - Discuss cover image, object, or tactile cue and title to introduce vocabulary - Use visual maps or story maps to introduce the story Establish purpose for reading: fun and/or learning objectives Rules for Answering Comprehension Question Things to Consider - Are you using symbols demonstrated through an assessment process as being understood by the student? - Have you identified key aspects of the story and vocabulary to introduce to the child before you begin reading the story together? - Are you allowing enough time for the student to respond? - Are you taking into consideration issues such as clutter, contrast, etc. when presenting literacy materials?

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With a dataset's average and standard deviation, we can find the probability of getting a data point of any particular value. We can do this using the rules for normal probability, represented graphically by a bell curve. The Bell Curve A "normal distribution" refers to a data set with values that occur in a bell-shaped pattern, increasing in value and frequency toward a mean, and then decreasing in frequency toward higher values. A distribution that is not normal is is data set is skewed. A skewed data set has more values are concentrated either higher (right) or lower (left) than the mean. The values in a normal data set are distributed symmetrically on both sides of the mean. Income is an example of a positively (right) skewed data set. There are more people in lower income than higher income groups: Life expectancy is an example of a negatively (left) skewed data set. There are more people expected to live until higher ages than lower ages: You can test for skewness to see if your dataset is normal or skewed. A non-normal distribution can also be skewed up "peaked" or down "flattened", meaning more values are located towards the tails (ends) or around mean (middle) of the curve. This measurement is called Kurtosis. You can test for kurtosis to see if your distribution is platykurtic or leptokurtic. The bell shape is reflected in the outline of the graphs of a frequency distribution, such as a histogram. Here is a histogram of the test scores for a class of students in our previous example: Our data set is approximately normal (slightly skewed left and slightly platykurtic, but testing shows it is not significant). Using the Bell Curve to Find Probability The bell curve of a data set with a normal (or approximately normal) distribution can be standardized so that the mean is equal to zero and each standard deviation is equal to one. The test scores are converted to z-scores - which are their number of standard deviations away from the mean. The area under the curve is equal to 1 or 100%. An important rules in statistics (called the Empirical Rule) states the following for all "normal" populations: 68% of the data falls within 1 standard deviation of the mean. 95% of the data falls within 2 standard deviations of the mean. 99.7% of the data falls within 3 standard deviations of the mean. Remember our example population of student test scores: Using our mean and standard deviation, we can calculate the following: 68% of the scores fall between 6.08 to 8.92 points. 95% of the scores fall between 4.36 to 10.64 points. 99.7% of the scores fall within 2.64 to 12.36 points. This method of standardizing scores (calculating how many standard deviations each score is away from the mean), allows us to find the probability of scoring particular values. For example, we now know that there is a 95% of scoring between 4.36 to 10.64 points. Conversely, there is a 5% chance of that student a student received a score outside of that range (less than 4.36 or higher than 10.64). Next, let's learn more about the Z-Distribution, and how to use the Z-table (or technology) to find the probability of any value in a dataset! Contact us for practice materials regarding standard deviation, the bell curve, the empirical rule, normal probability, and more.

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