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Argilla Warehouse 16

In Drawing a square we used the commands “move 50 steps” and “turn clockwise 90 degrees” four times each. To shorten this task we can use the repeat command. Wrapping blocks in a repeat allows us to reuse the logic. A computer can only draw straight lines, but we can create the appearance of a curved line by drawing a bunch of of tiny lines that, when connected together, look like a circle Since a circle has 360 degrees, we can create a circle by making 360 tiny lines, each one pixel long. After each line is drawn, we turn the pen 1 degree to the right. What if you wanted to draw a circle to the left? You could repeat the same commands except change the command “right” to the command “left.” We can also use the repeat command to easily make an equilateral triangle (a triangle in which the length of all three sides are equal). Since each of the internal angles must also be equal we can create a triangle by rotating the pen 120 degrees after each line is drawn.

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Before the lesson Download classroom resources - To create a stop motion animation Pupils should be taught to: - design, write and debug programs that accomplish specific goals, including controlling or simulating physical systems; solve problems by decomposing them into smaller parts - use sequence, selection, and repetition in programs; work with variables and various forms of input and output Pupils needing extra support: Can be in charge of referring back to their storyboard to make sure their group tells the story through the animation. Pupils working at greater depth: Should constantly review the animation to identify any frames that need to be deleted and should include multiple sets or characters in their animation.

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These worksheets, covering adding suffixes to words of more than one syllable, are an excellent way for children in Years 3 and 4 to revise and practise these spelling patterns. The worksheets include five different activities in which children look at spelling patterns, identify misspelt words and apply their spellings in context. They can be used within lessons, as an assessment or as a homework task. This primary resource is divided into five sections: This explains the rules on whether you double the last consonant when adding a suffix that begins with a vowel, depending on whether the the syllable is stressed or unstressed, eg ‘gardening’ vs ‘forgetting’, and asks students to find examples of each Circle the suffix words which are spelt correctly, add suffixes to the words listed, then add words with a suffix to each sentence Add suffixes to the words ‘upset’ and ‘suffer’ then use them in a sentence to describe the images Read each sentence and change the underlined word or phrase for a word which includes a suffix added to a word with two or more syllables Using the image as a prompt, write a short story about what happens. Add a suffix beginning with a vowel to each of the words given, and use them in your story. What is a suffix? Suffixes are letters, or groups of letters, that are added to the end of words to make a new word or change the meaning of word. - -ing: eating, running, saying - -ed: planned, walked, burned - -er: teacher, trainer, farmer - -est: highest, fastest, biggest - -ier: mightier, zanier, funnier - -ity: activity, equality, civility - -less: useless, sleeveless, witless - -ness: happiness, fitness, silliness National Curriculum English programme of study links - add prefixes and suffixes: using the spelling rule for adding –s or –es as the plural marker for nouns and the third person singular marker for verbs, using the prefix un–, and using –ing, –ed, –er and –est where no change is needed in the spelling of root words [for example, helping, helped, helper, eating, quicker, quickest] - read words containing common suffixes - add suffixes to spell longer words, including –ment, –ness, –ful, –less, –ly - apply their growing knowledge of root words, prefixes and suffixes (etymology and morphology) as listed in English Appendix 1, both to read aloud and to understand the meaning of new words they meet - use further prefixes and suffixes and understand how to add them - apply their growing knowledge of root words, prefixes and suffixes (morphology and etymology), as listed in English Appendix 1, both to read aloud and to understand the meaning of new words that they meet. - use further prefixes and suffixes and understand the guidance for adding them

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Many poor teenagers had to go to work early in their lives to ease the burden of their families. Most of the teenagers found jobs as indentured servants in the homes of more prosperous people. Indentured servitude meant that one would work for three to seven years in exchange for food and other necessities, and apprenticeship. During difficult times, even the adults would work as indentured servants as fewer positions were available. Most of the workers were immigrants from other nations who had come to seek work in America. Consequently, they agreed to work for more than four years to work and pay for their tickets. This study evaluates the concept of ‘indentured servitude’ and what made it an ethical act for both the master and the servant. Indentured servitude was the preferred method of survival for most slaves in early 1600 because it provided incentives for both the servant and the master. The leaders of each colony knew that labor was essential for economic gains, therefore, they provided the servants with survival incentives such as basic needs in the form of contractual agreement with the master[a1]. In some states, such as Maryland and Virginia, the system of ‘headright’ was adopted where each leader would be awarded 50 acres of land for each laborer brought across the Atlantic. Additionally, the leaders of the colony received services from the workers for the entire indenture period. The systems seemed to benefit the indentured servant too since each one of them would have their fare paid for by the master. Moreover, they signed a contract that would stipulate the length of the servitude which was in most cases five years. Therefore, the servants agreed to the terms because they were supplied with accommodation, food, and clothes while serving in the Master’s field. The servant would receive servant dues upon completion of the contract or an arranged pre-termination bonus which could be money, a gun, or basic commodities. Less than 50% of the indentured servants completed the full term of servitude because many terminated their contracts due to harassment from their masters. Shaw and Jenny (2018), illustrate that some servants were able to possess the land in the early century after they completed their contracts and were free men. However, it was only under tough circumstances where the servants would acquire land in Europe. According to Sharron (2018), the process of servitude would be very perilous although they had hoped for a brighter future in Europe, the conditions of the camps and harassment by the masters were incomprehensible and at times life-threatening. The masters ensured that they would make the most out of the servants as well as maintain them for as long as they preferred. Additionally, servants were displayed as cattle in a market, and those who were not bought right away were placed in merchant’s buildings.[a2] Indentured servitude seemed ethical because of the nature of the agreement between the servant and the master that was based on contractual terms. However, on arrival, the indentured servants were publicly announced for sale on the newspapers as commodities for enhancing productivity in farms. Most immigrants preferred indentured servitude because they were promised of a better life abroad and the possibility of owning land in Europe was rear, although it never happened for many of them. Shaw, Jenny. “Indentured Migration and the Servant Trade from London to America, 1618–1718:” There is Great Want of Servants.” by John Wareing.” The William and Mary Quarterly75.1 (2018): 187-189. [a2]What do you mean?This doesn’t make sense

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So after looking into the Datatypes,we got is What are Conditional Statements in Python?and why do we need them? The reasons are: Conditional Statement in Python perform different computations or actions depending on whether a specific Boolean constraint evaluates to true or false. Conditional statements are handled by IF statements in Python. Decision making is required when we want to execute a code only if a certain condition is satisfied. The if…elif…else statement is used in Python for decision making. so we have different decision making statement they are if condition: code() age=12 if age<21: print("you are under age") This is how we use the if statement if condition: code() else: code() here if the condition in the 'if' becomes true,then it executes code(1) if the 'if' condition is false then the code(2) is executed Age =11 if age<21: print("you are under age") else: print("you are an youngster") so next in the table we have if condition0: code() elif condition1: code() elif condition2: code(2) else: code() this is the syntax of the elif as we see if the condition in the 'if' : false the next condition is checked which is in elif block, if the conditions true the code will be executed,And so. so lets see an Ex: num=1,num=-23,num=0 if num > 0: print("Positive number") elif num == 0: print("Zero") else: print("Negative number") The nested is to do the condition checking simultaneously. 2.Nested if else A nested if is an if statement that is the target of another if statement. Nested if statements mean an if statement inside another if statement.Yes, Python allows us to nest if statements within if statements. we can place an if statement inside another if statement. the syntax will be if (condition1): code() if (condition2): code() a= 1001 if a> 100: print("Above 100") if a > 1000: print("and also above 1000") so the next is using one “if else” statement inside other if else statements it is called nested if else statement. the syntax for this is if(condition): if code if(condition): if code else: else code else: else code lets see an Ex: a=1456 if a> 100: print("Above 100") if a > 1000: print("and also above 1000") else: print("and also below 1000") else: print("below 100") so these are the conditional statements in the pyhton so once again why do we use these conditional statements? Conditional statements are also called decision-making statements. We use those statements while we want to execute a block of code when the given condition is true or false. well see you in the next post.

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SS2: PHYSICS - 1ST TERM Scalars & Vectors | Week 15 Topics|1 Quiz Equations of Motion | Week 23 Topics|1 Quiz Projectile | Week 35 Topics Equilibrium of Forces I | Week 44 Topics Equilibrium of Forces II | Week 54 Topics Stability of a Body | Week 64 Topics|1 Quiz Simple Harmonic Motion (SHM) | Week 74 Topics Speed, Velocity & Acceleration & Energy of Simple Harmonic Motion | Week 85 Topics|1 Quiz Linear Momentum | Week 96 Topics|1 Quiz Mechanical Energy & Machines | Week 102 Topics|1 Quiz Moment of a Force When taps are opened, a turning effect of force is experienced, likewise, when doors are opened, the applied force brings about a turning effect about a point or hinges attached to the wall of the door. The turning effect experienced in each case is called the moment of a force. The moment of a force about a point (or axis )O, is the turning effect of the force about that point. It is equal to the product of the force and the perpendicular distance from the line of action to the point or pivot. Moment = Force x Perpendicular distance of pivot to the line of action of the force = Newton x Metre Its unit is Newton metre (Nm), hence, it is a vector quantity. If the force is inclined at an angle θ. Moment = Fdsinθ The magnitude of moments depends on: i) The Force applied iI) The perpendicular distance from the pivot to the line of action of the force. When more than two forces act on a body, the resultant moment on the body about any point can be obtained using algebraic moments using the clockwise moment and anticlockwise moments about the same point. If the clockwise moment is taken as positive and the anticlockwise moments are negative. ∴ Clockwise moment about O = Anticlockwise moment about O \( \scriptsize F_1 \: \times \: X_1 = F_2 \: \times \: X_2 \) \( \scriptsize F_1 \: \times \: X_1 \: -\: F_2 \: \times \: X_2 = 0 \)

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Plate movement is the sliding of Earth’s lithosphere (Earth’s outer layer) over the mantle layer. This action results in the formation of Earth’s features, such as mountain ranges and continental drift. Generally, plate movements are influenced by different forces on the Earth’s plates; these forces may be classified as either convergent, divergent, or transform. Convergent plate movement results from the action of converging forces exerting pressure on the lithosphere and Earth’s crust, thus causing a collision on their boundaries. This, in turn, results in the submersion of one plate beneath the other. When this force is exerted on two continental plates, which brings about the creation of mountain ranges; however, when these forces are exerted on two oceanic crusts, they cause fissures, which allow magma to flow from the mantle, thus forming volcanoes. In addition, these forces may occur between the oceanic plate and continental plate, giving rise to the submersion of the oceanic plate below the continental plate. Divergent plate movement occurs in oceanic plates when diverging forces influence the seafloor plates to move away from each other. This causes an oceanic crust to form from the Earth’s mantle, mainly as a result of the splitting of the plates. Transform, or lateral slipping, plate movement occurs during the movement of two plates side by side. Although these plates may face each other, they move in different directions but still remain close to each other. As a consequence, enormous friction is produced, which makes the plates stick and then slip away from each other. During the release of the plates from each other, a sudden Earth tremor occurs, known as an earthquake. Therefore, transform forces are the main causes of Earth tremors or earthquakes.

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Lesson Plan: Perimeter of Rectangles and Squares Mathematics This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to find the perimeter and area of squares and rectangles. Students will be able to - understand that the perimeter of a shape is the distance around its edge, - understand that the area of a shape is the amount of space inside it, - find the perimeter or area of a square or rectangle from a diagram by counting squares, - describe the formulas for finding the perimeters of squares and rectangles using words, - find the perimeter of a square or rectangle given its dimensions, - find the side length of a square given its perimeter, - find the length or width of a rectangle given its perimeter and other dimensions, - find the perimeter of a rectangle in which the length and width are given in different metric units, - find the area of a square or rectangle given its dimensions, - find the length or width of a rectangle given the other dimensions and its area. Students should already be familiar with - how to recognize squares and rectangles, - converting between metric units for length, - adding, subtracting, multiplying, and dividing whole numbers within 1,000. Students will not cover - calculating perimeters or areas of squares and rectangles where the side lengths are noninteger values, - calculating perimeters or areas of any other 2D shapes, - conversion of area units.

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This article covers how to use the if else statement in Python. In fact, An if else Python statement evaluates whether an expression is true or false. If a condition is true, the "if" statement executes. Otherwise, the "else" statement executes. Python if else statements help coders control the flow of their programs. Python Conditions and If statements Python supports the usual logical conditions from mathematics: - Equals: a == b - Not Equals: a != b - Less than: a < b - Less than or equal to: a <= b - Greater than: a > b - Greater than or equal to: a >= b Python Nested if statements We can have a if...elif...else statement inside another if...elif...else statement. This is called nesting in computer programming. Any number of these statements can be nested inside one another. Indentation is the only way to figure out the level of nesting. They can get confusing, so they must be avoided unless necessary. Python Nested if Example '''In this program, we input a number check if the number is positive or negative or zero and display an appropriate message This time we use nested if statement''' num = float(input("Enter a number: ")) if num >= 0: if num == 0: Output 1 will give: Enter a number: 5 Output 2 will give: Enter a number: -1 Output 3 will give: Enter a number: 0

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On July 17, 1830, the Cherokee nation published an appeal to all of the American people. United States government paid little thought to the Native Americans’ previous letters of their concerns. It came to the point where they turned to the everyday people to help them. They were desperate. The Indian Removal Act was signed in 1830 by President Andrew Jackson to remove the Cherokee Indians from their homes and force them to settle west of the Mississippi River. The act was passed in hopes to gain agrarian land that would replenish the cotton industry which had plummeted after the Panic of 1819. Andrew Jackson believed that effectively forcing the Cherokees to become more civilized and to christianize them would be beneficial to them. Therefore, he thought the journey westward was necessary. In late 1838, the Cherokees were removed from their homes and forced into a brutal journey westward in the bitter cold. The hardships of the sufferable journey can be observed by three separate accounts form a Cherokee woman, a Cherokee slave, Trail of Tears Native Americans experienced a dramatic change in the 1830s. Nearly 125,000 Native Americans who lived on inherited land from ancestors of Alabama, Georgia, North Carolina, Tennessee, and Florida were all cast out by the end of the decade. The federal government forced the natives to leave because white settlers wanted an area to grow their cotton. Andrew Jackson (President of the U.S. during this time) signed into law, the Indian Removal Act, authorizing him to grant unsettled lands west of the Mississippi River in return for native lands within state borders. In President Andrew Jackson’s Message to Congress on December 6,1830, it was said “Cherokee nation occupies its own territory and no Georgia citizens have the right to enter” (Worcester). The Indians had the right to keep their land but president Jackson took their land away. The Indians also had their rights being violated by the government in other ways. In America History of our Nation their rights were also being violated because the government had a law signed forcing the Creeks to give up most of their land (page 357). Their rights were again being violated, showing another reason why the Indian Removal Act should not have been The Trail of Tears In 1835 the New Echota Treaty signed into effect that the Cherokee people would sell their land to the American government and abdicate land by May 23, 1838. This paper follows the tragedy than Sue 's this unjust theft of land and lives that were taken from the Cherokee people. The first group in the story is made up of the men who met with the US government to negotiate the details of the New Echota Treaty. In June 1830, Chief John Ross went to defend Cherokee rights before the U.S. Supreme Court after the state of Georgia passed legislation that John Ross claimed to "go directly to annihilate the Cherokees as a political society." Georgia retaliated, claiming that the Cherokee nation could not sue since they were not a foreign nation with a constitution, therefore the case should not be brought to court in the first place. This brought upon the Supreme court case Cherokee Nation v. Georgia in 1831. The conclusion of this case, decided upon by Judge John Marshall was that "the relationship of the tribes to the United States resembles that of a ‘ward to its guardian '. " I disagree with this outcome. Indian removal President andrew jackson signed a law on may 28, 1830. The law was called the Indian Removal. A few tribes went peacefully but some did not want to go and leave their home. In 1838-39 the cherokee were forcefully removed from their homes. 4,000 cherokee died on this trip which became known as “The trail of Tears”. After imposing political and military action on urging the Native American Indians from the southern states of America, President Andrew Jackson decided it was time to enact the Indian Removal Act of 1830. The Indian Removal act of 1830 proclaimed that all Native Americans living east of the Mississippi River were to be forced to move west of the Mississippi River where the region of the Louisiana Purchase remained. This land set aside for these Native Americans was known as the “Indian colonization zone”. Because some of the Indian tribes refused to leave their homelands, “As a result, wars broke about between the U.S. Government and Indian Tribes”(xbox360). The Indian Removal Act was originally created to have the Native Americans vacate There were tribes known as the Five Civilized Tribes that lived in the regions of Georgia, Alabama, Mississippi, Arkansas, and Florida. These tribes were the Cherokees, Chickasaws, Choctaws, Creeks, and Seminoles. They all lived in peace with each other and adopted many cultural ways and customs of the whites. Unfortunately, some Americans believed forcing the tribes, specifically the Cherokees, out of their regions would be a great personal achievement. Georgia was first on the list to seize and to do so the president gave the Cherokees a “choice”. This improves the reader's understanding of the Americans want for land and helps contextualize the arguments made by Wallace. Lastly, Wallace does a good job of not showing a bias towards or against Jackson. He explains Jackson’s personal reasons for putting the Indian Removal Act in motion, but also presents other points. He explains economic factors and factors from outside of the states that influenced the treatment of Natives. The facts presented in this article agree with the prior consensus of this The Trail of Tears in 1839 was a horrific event that removed thousands of Native Americans from there homes. They were forced to travel a thousand miles on foot to a new land. Thousands of lives were lost along and after the journey. The removal effected the Cherokees greatly and it still effects them today. They Trail of Tears was dangerous, deadly, and many didn 't The Trail of Tears occurred in 1838 and was put in play by the then reigning President Andrew Jackson. “Gold fever” and a thirst for expansion by the white population made them turn on there Cherokee neighbors. The Native Americans and white settlers had once tried to live in harmony even with the altering of their culture, but the greed and unfortunate disapproval of the Native Americans and their way of life made the whites want to have a further disconnection from them. Many people opposed the removal and even had court cases to try and appeal the removal. People such as Daniel Webster, Henry Clay, and Chief John Ross, who was of Cherokee descent. All treaties previously established between the Cherokee and the United States government were tossed to the wind and Indian villages were set on fire and destroyed. The man they had once considered an ally was of no help as President Andrew Jackson ignored the pleas of the Cherokee and even withdrew all federal troops from their sacred territory. Nothing but gold was sacred to the Jacksonian democracy. One year after the discovery of gold in 1830, political officials in Georgia decided to force their state laws upon the Cherokees. While the Supreme Court first Imagine having to walk over 1200 miles because someone else wants you land. In 1820 five Native American tribes the Chickasaw, Choctaw, Seminole, Cherokee, and Creek Indians were invaded by all of the white people who came to the U.S from Europe, and the white men got very settled. Ever since the white men showed up to the U.S. there was conflict with the Native Americans. The Indian Removal Act is when southern Indian tribes formed their removal of the Natives and forced them to leave all of there stuff. I believe that the Indian Removal Act is a step in the wrong direction because we were not treating the Native Americans like human beings, it went against the constitution, and jackson wanted to build a wall to separate. xIs it wrong to kick someone out of their own home when they didn’t do anything wrong? The Cherokee was in that same situation. The Cherokees’ situation was just like taking a cell phone ,which is dear to a human, away. They were kicked off their own land. They had done nothing too bad, but the Georgians wanted them to leave. The Supreme Court even allowed them to stay, but the new settlers still wanted them out. The Indian Removal isn’t justified and the Indians should have stayed in Georgia because it was their own land, staying would help their health, and only a few signed the treaty.

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12.2Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect? Hint: The mass of the Hydrogen atom is less than the mass of the -particle. Step 1: Compare the mass of the Hydrogen atom with the mass of the -particle. The mass of hydrogen is less than the mass of incident -particles . Thus, the mass of the scattering particle is more than the target nucleus (hydrogen). Step 2: Analyse the scattering angle in this case. In the alpha-particle scattering experiment, if a thin sheet of solid hydrogen is used in place of a gold foil, then the scattering angle would not be large enough and the -particles would not bounce back if solid hydrogen is used in the particle scattering experiment.

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What is the “Class 5 Maths Chapter 6 Worksheet”? This worksheet will be discussing the factors. This worksheet will become a guide on how to find the factor of a number.. What is a Factor? A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product. How will the “Class 5 Maths Chapter 6 Worksheet” help you? This worksheet will help you in enhancing your skills on how to determine the factors of any number. Instructions on how to use “Class 5 Maths Chapter 6 Worksheet” Use this worksheet to enhance your ability in determining the factors. After a short discussion, an activity will be given to the learners to find the factors of the given number.. An activity will also be given to the learners to complete the factor trees. Lastly, the learners will be asked about the most important concept when it comes to real life application. Being able to determine the factors will be used in the higher topics of mathematics. If you have any questions or comments, please let us know.

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A recent study facilitated by Bedrock Learning showed that 97% of teachers said grammar was vitally important for teaching and aids directly in a reader’s comprehension. The understanding of grammar forms a foundation for clear and confident communication, which allows every student to understand the English language to a much greater depth. In this article, we will look at some basic grammar rules behind adjectives and present some exercises to help your students understand them. What is an adjective? Simply put, adjectives are words which modify nouns and pronouns. They are one of the most widely used aspects of grammar and are most often called “describing words”. In the classroom, learners are encouraged to use adjectives in their work to provide more detail in a sentence, as well as making the writing more engaging for a reader. Often, younger learners can get carried away with the action and movement of a story, and forget to think about what things look like, or where the story takes place. Adjectives allow writers to provide these descriptions to a reader and communicate how a story looks in their head to their readers. From an early age, learners use simple adjectives in their writing to communicate how something looks or feels, using words such as “blue” or “scary” to provide detail - for example, a blue, scary ghost. However, from Year 3 onwards, learners are expected to select more sophisticated adjectives, using synonyms to craft the most effective description. Your learners will discover that changing a phrase such as “the scary man” to “the menacing man” gives a new meaning to the phrase. Though “scary” and “menacing” are considered synonyms, only the latter provides further clarification and gives the phrase much more depth. Adjectives are words which learners encounter at every stage of their education and are vital when explaining something or helping a learner to visualise a story. In sentences, adjectives are used to give clarification about a noun and can be placed in different positions to change the effect. Although we usually use adjectives to add more detail, there are many types of adjectives, all of which we use every day. Here are some examples of these adjectives in use: - To describe - The charming man, the fluffy dog - To count - Both of my friends, the eighth slice of cake - To quantify - Two sports cars, five eggs in the nest - To demonstrate - That flower, those houses - To interrogate - Which umbrella? - To possess - My umbrella is over here - To exclaim - What an idea! The everyday English speaker may not be aware that some of these words are adjectives, or how often they are used in everyday conversation. Learning about these adjectives is vital for effective communication and allows students to both describe the world around them with accuracy, as well as understand how this world is communicated to them. Adjectives and nouns Adjectives and nouns always appear together. A noun is a “naming word” for objects, people, places and more, acting as the subjects or objects of a sentence. An adjective is a word that modifies this noun and gives it a new quality through a new description. When selecting an adjective, it is important to choose one which describes something new about a noun. If you describe water as wet, you are adding nothing new to the noun and, as a result, the adjective has no purpose. However, if you describe water as warm, or fizzy, the noun takes on a new quality, as these aspects are not already known. Sometimes, nouns can act like adjectives. We can describe a noun with another noun, such as a boat race, or a sports team. In these phrases there is no adjective, but the noun has been modified by its reference to another noun. Similarly, we can describe a group of people as the elderly, or the rich. These are known as adjectival nouns, and we can spot these by looking for the article “the” which always appears first. Types of adjectives The most common misconception about adjectives is that there is only one type: the “describing word”. Though this is the most frequent use of an adjective, it is far from its only use. Here, we will explore the many types of adjectives, and how they can be used by students and teachers alike. The descriptive (simple) adjective A descriptive adjective is the type of adjective you are most likely to encounter in the classroom, as well as in everyday conversation. Descriptive adjectives add meaning to a noun or pronoun by describing its qualities which do not appear otherwise in the sentence. There are thousands of adjectives to choose from, and each of them changes the noun they describe. To find where a descriptive adjective is used in a sentence, it is important to identify the subject, the object, and the verb. Take this sentence for example: - He wants to buy an enormous house. “He” is the subject of the sentence, as a subject performs an action. As the action of the sentence is buying, this makes “buy” the verb in the sentence. This makes “house” the object, as the house is the thing being involved, or impacted, by the action. Now that we know where the object, subject, and verb are placed, we can look at the object in focus. The house is described as “enormous”; this describes to a reader what the house looks like. The descriptive adjective can come in two forms. The first, which a learner is most likely to encounter, is the simple adjective. A simple adjective can describe emotions, taste, appearance, colour, and shape: - The green book. - The scary darkness. - The knights of the round table. The compound adjective The second form is a compound adjective. These descriptors are adjectives combined with a hyphen, and are used the same way as simple adjectives: - The mouth-watering smell of dinner. - A right-handed student. Both types of descriptive adjectives provide new information about a noun, helping a reader to learn more about the details of a sentence. Each of them provides a quality to the noun, which was not present before, and reveals a deeper meaning to the information within a sentence. Discover our grammar curriculum Bedrock Grammar immerses students in engaging learning experiences, using stories, video, interactive activities and scaffolded writing opportunities. The numerical adjective Rather than describing the quality of a noun, numerical adjectives denote the quantity of a noun present. The use of numerical adjectives is important for maintaining clarity and gives exact information regarding amounts: - There are six apples on the tree. - I am the second in line. - Only twelve miles to go! The examples above are called definite numerical adjectives, as they provide exact information about the number of things in a context. Not only do they provide clarity in English, but this adjective technique highlights the link between improving literacy and success in Maths. The quantitative adjective Quantitative adjectives are used when nouns are uncountable in nature, whereas definite numerical adjectives are only used when something is countable. If we look at the sentence “Friday is the fifth day of the week”, we know that fifth is a definite numerical adjective, as it can be counted. Words such as few or little are quantitative adjectives, as they refer to an amount that cannot be counted. These adjectives are also known as indefinite numerical adjectives, as they provide inexact, or tentative, information about the number of people or things. Examples of a quantitative adjective are: - All of my sweets are gone. - Several apples fell from the tree. - Any colour will do! Unlike definite numerical adjectives, these adjectives do not refer to any specific amount. Instead, they are used to provide a general amount, a quantity of a noun rather than the number. The proper adjective To understand the proper adjective, you must first understand the proper noun. A proper noun is the name of a specific person or place, such as Elizabeth, Spain, or Shakespeare. Some proper adjectives, like the examples given above, can be modified into an adjective, and you can do this in two ways: Shakespeare is a specific person, and his name is a proper noun. As Shakespeare had such a unique writing style, the adjective Shakespearean can be used to describe writing which is like Shakespeare’s own. - That movie was amazing! It had a brilliant Shakespearean writing style. Spain is a specific place, and its name is a proper noun. As people from Spain are referred to as Spanish, it can be modified into a proper adjective. - I saw my Spanish friend last week. Proper adjectives are used to make a sentence as specific as possible. It is important to remember that all proper nouns begin with capital letters, just like the proper nouns they are modified from. The demonstrative adjective The demonstrative adjective is a less used adjective and is sometimes called a determiner. The demonstrative adjective identifies the position of a noun or pronoun, and gives information about its distance from the speaker. The four demonstrative adjectives are “this”, “that”, “these” and “those”. Like the adjectives so far, demonstrative adjectives come before the noun in the sentence: - This bottle is by my feet. - That bottle is over there. - These shoes are next to me. - Those shoes are on the shoe rack. Demonstrative adjectives work with time as well as with objects. The sentence, “This evening was amazing!” tells us that the “evening” was close to the speaker, whereas the sentence, “That weekend was so boring!” tells us the weekend happened in the past. However, a student might make two mistakes here: Firstly, it is important to remember that these adjectives are not the same as demonstrative pronouns. Adjectives always refer to a noun (“these flowers”), whereas a demonstrative pronoun is on its own. In the phrase “Ow! That is sharp!” we see “that” used as a pronoun, as it replaces the name of the object. Secondly, it is important to remember the number of objects that you are talking about. “These flower in my hand” is incorrect, as there is only one flower. “Those type of things” is incorrect too, as “type” should be a plural. Learners may stumble remembering which demonstrative adjectives go with singular and which with plural nouns. The interrogative adjective Interrogative adjectives are unique, as they modify a noun by asking a question. Some examples of interrogative adjectives are “what”, “which” and “whose”, and these are also known as interrogative determiners. To know which of these to use in a question, you need to know which way the question should be answered. If you do not know the options available, you could ask “What options are there?” If you know the options, you could ask “Which options are available?” If the option is a person, you could ask “Whose options are these?” - Whose homework is this? - What kind of snack would you like? - Did he ask you which movie is your favourite? A student may make the mistake of confusing an interrogative adjective with an interrogative pronoun. An interrogative pronoun is followed by a verb, rather than a noun, and substitutes for a noun in a question. In the phrase “Which did you want?”, the word “which” has replaced the noun in the sentence, rather than modifying it. The possessive adjective The possessive pronoun sits before a noun or a pronoun to indicate who, or what, owns it. Possessive adjectives are also known as possessive determiners. The most common possessive adjectives are “my”, “your”, “his”, “her”, “its” and “our”. These all correspond to the pronoun of the subject in the sentence: - John put his plate away. - Sarah and James took their football to the park. - I hid my new game. In each of these examples, we see the ownership of the object in relation to the subject. When finding out which possessive adjective to use, it is crucial to know the pronoun of the person or thing in the sentence. If a dog was itchy, it would scratch its ear. If your spaniel, Susan, was itchy, she would scratch her ear. Here, we can see that the adjective changes depending on the gender of the subject. If the subject does not have a gender, you can use “its” (for inanimate objects) or “their” (for groups, or when the gender is not known). A potential error your learners may make when learning possessive adjectives is spelling. Some of the most used possessive adjectives are homonyms to different words, and it is important to make the distinction between them in the classroom. - Today is your special day! - The dog wagged its tail. Both are often confused with the contractions you’re and it’s, which do not make grammatical sense when used in these sentences. To help your students remember which to use, think of the contractions being full words. If you heard someone say, “Today is you are special day!” it wouldn’t make any sense. The exclamatory adjective Exclamatory adjectives are a combination of adjective and exclamation and are used to express heightened emotions. If you are feeling especially happy, you might shout out “What a wonderful day!”. In this sentence, the word what is an exclamatory adjective, a word which amplifies the emotion being felt alongside a noun. - How smart is Nadia! - What a beautiful cave painting! Each of these adjectives refers to the named noun in the sentence and expresses how a speaker is feeling about them. In the first sentence, the speaker expresses surprise and happiness about the intelligence of Nadia. In the second, the speaker is in awe, stressing the importance of the painting. Often, these exclamations are paired with descriptive adjectives. This allows for a reader to understand the aspect of a noun that a speaker is highlighting. If someone shouts, “What a beautiful rendition of that song!” we learn that the speaker is happy about the song they are hearing, because they find it beautiful. Transform literacy through grammar Bedrock Grammar is here to make a difference. It teaches a deep understanding of language and how it works. Adjectives or adverbs? Two groups of words which are often confused are adjectives and adverbs. As we have already seen, adjectives modify nouns to give them more detail and meaning. The primary difference between them is that an adverb cannot modify a noun. However, an adverb can modify verbs. An easy way to tell these apart is the suffix -ly, which appears at the end of most adverbs: - The large man scratched his head thoughtfully. - I think I got the question wrong. I wasn’t thinking quickly! In these examples, we can see adverbs in action. Rather than describing a noun to provide visual information, an adverb tells us how something occurs, or how something is done. In most cases, it does not make sense grammatically to use an adverb before a noun, so we find them after the verb in a sentence. Rules for using adjectives Now that you know all about adjectives, it is important to make sure you know where common errors occur, and how to ensure your students don’t trip up. Take the sentence below: - I want to go to the Tudor blue old big house down the road! For native speakers of English, this sentence probably feels wrong, but it’s difficult to articulate why; this is because the grammar technique at play here is usually learned incidentally, rather than taught explicitly. The rule of order of adjectives is being broken here. When listing more than one adjective, you begin with a quantity, then your opinion, then size, then age, then shape, then colour, then material, and finally the qualifier. When following this rule, the sentence becomes: - I want to go to the big old blue Tudor house down the road! This sentence sounds more natural to speak, even if you had not known the rule beforehand. This hierarchy of importance is something we learn incidentally as an English speaker, although people are unsure how this rule came to be. Even when we don’t use all of the categories, we continue to follow this order. How many adjectives should you use? There is no definite answer, but there are ways to find out for yourself. Which of these sentences do you prefer? - A face appeared at the window. - A scary, pale, ghoulish face appeared at the window. When comparing these two sentences, the first sentence feels punchier, as the information in the sentence is given to you much quicker. However, the first sentence does not give us any more information about the face. Was it a friend at the window, or was it a ghost? Only the second sentence tells us. As a result, it is important to find a balance between delivering information quickly, and making sure a reader knows all the important aspects of the moment. If you hear a knock at the door, you might go and answer it. However, if you hear a loud, thumping knock at the door, you might think twice before you open it. This links to lessons you might deliver on the effects of sentence structure. Forming adjectives from verbs In English, it is possible to create an adjective from a verb, which results in participles. A present participle ends with -ing, whereas a past participle ends with -ed: - The movie was exciting. - I was excited by the movie. In the first sentence, a present participle is used. This is because the sentence describes the effect the movie has on someone. However, the second sentence uses a past participle as it describes how someone was affected by the movie. Remember, when you are describing an inanimate object, you use a present participle. However, when you describe a person, you use a present participle: - I don’t find books interesting. - Really? I am very interested in books. Teach grammar effortlessly Bedrock's core curriculum uses a smart self-marking curriculum to embed grammar knowledge. Below are some activities which you can use in the classroom, each of which can help your learners become more comfortable with adjectives! Ask your learners to describe themselves in a sentence using adjectives! Remember to make sure they use the rule of order. You could begin with describing yourself, then maybe move on to family members, fictional characters or celebrities. Who am I? Create a series of riddles for your learners and see if they can figure out the animal from the adjectives. Some examples are below: - I am fluffy and fast, and I have a wagging tail. I am a dog! - I am a fast swimmer, and I have a sensitive nose. I am a shark! - I am fluffy and striped, and I have a painful sting. I am a bumblebee! - I am fast and striped, and I am black and white all over! I am a zebra! - I am slow and slimy, with a large shell on my back. I am a snail! Simplify the sentences Create a series of sentences, in which there are far too many adjectives. Ask your students to take out the unnecessary adjectives from each sentence. Ask them to explain why they have removed each adjective and see if they understand what makes a word necessary. Some examples are below: - The scruffy, small, thin, old, spotted dog. - The beautiful, huge, clean Elizabethan mansion. - The delicious, colourful Italian dinner. - The rusty, broken, old, blue, metal car. If you want to make this activity more difficult, you can also place the adjectives in a random order. See if your students can order them correctly! Match the adjectives Create a series of synonyms for adjectives on cards and ask your learners to pair up the adjectives which have the same meaning. Some examples of pairs are below: - Angry and furious. - Smart and intelligent. - Funny and humorous. - Warm and welcoming. Give learners a pair of adjectives and ask them to identify which of the adjectives is more intense. Alternatively, you can ask your learners if a word could be made more intense, or if a word could be made even softer. Some examples are: - Pop or explode. - Singe or ignite. - Little or tiny. - Large or massive. - Quick or rapid. How Bedrock Learning teaches adjectives Bedrock’s grammar curriculum teaches simple adjective rules at first, introducing learners to the concept of describing nouns, before moving onto more complex adjective rules and techniques. Each lesson is taught through engaging video activities and bespoke prose, before learning is solidified through contextualising activities and mastery tasks. Teachers and educators can monitor progress through consistent low-stakes assessment, with data processed and presented neatly in the reporting area of your dashboard. All prose and teaching is differentiated for primary and secondary, solidifying necessary grammar skills as learners progress through school. Accurate grammar is a skill necessary for your learners’ success throughout their academic careers, and their whole lives, but it isn’t always the most engaging lesson to teach. Through Bedrock’s video teaching and human narration, teachers can save time on marking while knowing their learners are being motivated to learn grammar independently, gaining the mastery they need to apply their knowledge to reading and writing. Bedrock’s grammar curriculum sits alongside vocabulary to form a comprehensive literacy solution. To find out more about how grammar can benefit your primary and secondary learners, click the link below and start your free trial of Bedrock’s core curriculum.

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9.4: Impulse-Momentum Theorem The total change in the motion of an object is proportional to the total force vector acting on it and the time over which it acts. This product is called impulse, a vector quantity with the same direction as the total force acting on the object. By writing Newton's second law of motion in terms of the momentum of an object and the external force acting on it, and simultaneously using the definition of the impulse vector, it can be shown that the total impulse on an object is equal to its net change in momentum. This mathematical relationship is called the impulse-momentum theorem, and it is true even if the force acting on the object varies with time. For instance, in ice hockey, the puck experiences a significant impulse during a slap shot. A considerable force acts on the puck for less than a second, causing a change in the ball's velocity and hence its momentum. The difference in momentum is added to the initial momentum to calculate the final momentum. According to the theorem, the change in momentum of the puck is equal to the impulse experienced by the puck. It is essential to note that an impulse does not cause momentum; instead, it causes a change in the momentum of an object. This text is adapted from Openstax, University Physics Volume 1, Section 9.2: Impulse and Collisions.

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Today, we are going to learn about proper nouns. Before we begin, let's define what a proper noun is so everyone has the same understanding. A proper noun is the name of a place, person or thing. (Have the students repeat the definition) 1. Ask the students to give you some examples of proper nouns. 2. Next, watch this video about proper nouns which will go into further detail about what it is (Insert link here). 3. After watching the video, hand out and go over the proper nouns worksheet (Insert link here). 4. Lastly, the students will choose one of their proper nouns and write a story about it. Have the students give examples of proper nouns and ask them questions about the worksheet. Assess their understanding of proper nouns by seeing what examples they give you and how they do on their stories. For children who are not quite ready to write a proper noun story, give them a proper nouns word search worksheet. (Insert link here) Have the students present their proper noun stories to the rest of the class. Word Search Worksheet:

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Plants are pretty much unique among living organisms because they can trap the energy of sunlight and use it to make organic molecules that are rich in energy. In this way they create their own fuel that has no unwanted byproducts and that fulfils all their energy needs. Imagine if humans could develop a similar photosynthetic surface that used only water, carbon dioxide and energy from the sun to make green fuels. Well, this is exactly what scientists from the University of Cambridge have been working on. Although renewable energy technologies such as wind turbines and solar panels have become significantly cheaper and more available in recent years, industries such as shipping remain wholly dependent on fossil fuels. Switching to green energy for an industry such as shipping is a tall order and the subject has received little to no attention in terms of changes that can be made to slow global warming. Around 80 percent of global trade is transported by cargo vessels powered by fossil fuels, so the contribution by this sector to climate change is probably not insignificant. For several years, Professor Erwin Reisner’s research group at Cambridge has been working to address this problem by developing sustainable solutions to petrol which are based on the principles of photosynthesis. In 2019, they developed an ‘artificial leaf’ that makes syngas – a key intermediate in the production of many chemicals and pharmaceuticals – from sunlight, carbon dioxide and water. Their prototype generated fuel by combining two light absorbers with suitable catalysts. However, it incorporated thick glass substrates and moisture protective coatings, which made the device heavy to transport and to deploy. “Artificial leaves could substantially lower the cost of sustainable fuel production, but since they’re both heavy and fragile, they’re difficult to produce at scale and transport,” said Dr. Virgil Andrei from Cambridge’s Yusuf Hamied Department of Chemistry, the paper’s co-lead author. “We wanted to see how far we can trim down the materials these devices use, while not affecting their performance,” said Reisner, who recently led a new research project aimed at slimming down the artificial leaves to make them more adaptable. “If we can trim the materials down far enough that they’re light enough to float, then it opens up whole new ways that these artificial leaves could be used.” For the new version of the artificial leaf, the researchers used technology from the electronics industry, where miniaturization techniques have led to the creation of smartphones and flexible displays, revolutionizing the field. The researchers faced the challenge of placing light absorbers onto lightweight substrates and then coating them with waterproofing material to protect them from water infiltration, all the while keeping the structure light enough to float. They overcame these obstacles by using thin-film metal oxides and materials known as perovskites, which can be coated onto flexible plastic and metal foils. The devices were covered with micrometer thin, water-repellent, carbon-based layers that prevent moisture infiltration. They ended up with a device that not only works, but also looks like a real leaf. And it floats on water. The researchers tested the photoelectrochemical (PEC) artificial leaves on the River Cam and have published their findings in the journal Nature. The experts report that their lightweight, leaf-like PEC devices can split water into oxygen and hydrogen (as happens in plant leaf cells during photosynthesis) and reduce carbon dioxide to produce fuel at rates comparable to those found in photosynthesizing leaves. In addition, the artificial leaves weight less than 100 mg cm−2 and can be scaled up to produce larger structures that can still sustain similar production rates. “This study demonstrates that artificial leaves are compatible with modern fabrication techniques, representing an early step towards the automation and up-scaling of solar fuel production,” said Dr. Andrei. “These leaves combine the advantages of most solar fuel technologies, as they achieve the low weight of powder suspensions and the high performance of wired systems.” This is the first time that clean fuel has been generated on water, and if scaled up, the artificial leaves could be used on polluted waterways, in ports or even at sea, and could help reduce the global shipping industry’s reliance on fossil fuels. While additional improvements will need to be made before they are ready for commercial applications, the researchers say this development opens whole new avenues in their work. “Solar farms have become popular for electricity production; we envision similar farms for fuel synthesis,” said Dr. Andrei. “These could supply coastal settlements, remote islands, cover industrial ponds, or avoid water evaporation from irrigation canals.” “Many renewable energy technologies, including solar fuel technologies, can take up large amounts of space on land, so moving production to open water would mean that clean energy and land use aren’t competing with one another,” said Professor Reisner. “In theory, you could roll up these devices and put them almost anywhere, in almost any country, which would also help with energy security.” Image Credit: Virgil Andrei

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Auxiliary verbs, also known as “helping verbs,” are a group of verbs used in English to help form different tenses, moods, voices, and aspects of a main verb in a sentence. They work in conjunction with the main verb to provide additional information about the action or state being described. The primary auxiliary verbs in English are “be,” “have,” and “do.” Nine modal auxiliary verbs are: can, could, will, would, shall, should, may, might, and must. - Be (am, is, are, was, were, being, been): It is used to form continuous tenses and passive voice. - Continuous tenses: He is eating. She was running. - Passive voice: The book is being read by Mary. - Have (has, have, had): It is used to form perfect tenses and perfect continuous tenses. - Do (do, does, did): It is used to form questions, negatives, and emphatic statements in simple tenses. - Questions: Do you like coffee? Does she play the piano? - Negatives: They do not know the answer. He did not finish his homework. - Emphatic statements: I do believe you. She did finish the race. Note that when using auxiliary verbs, the main verb is typically in its base form (infinitive form) without “to” (e.g., “go,” “eat,” “play”). Here are some examples of auxiliary verbs in action: - Present continuous tense: He is eating dinner. - Present perfect tense: She has already seen that movie. - Past continuous tense: We were playing in the garden. - Past perfect tense: They had finished their work before the deadline. - Future simple tense: I will call you later. - Future continuous tense: They will be waiting for us at the airport. - Modal verb + base form: He can swim. They should go now. Auxiliary verbs are crucial for constructing various sentence structures and conveying different nuances of meaning in English. Understanding how to use auxiliary verbs correctly is essential for creating well-formed sentences and expressing ideas accurately.

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Lesson 2C: Permutations Recall Example 1 in Lesson 2A in which customers were asked to choose an ice cream cone. The problem was to determine how many a customer could have when given one choice each of cone, ice cream, and topping. Because you have to choose cone - ice cream - topping in a specific order , this problem is called a permutation . Permutations are the focus of this Training Camp. By the end of this lesson, you should be able to determine, the number of permutations of n elements taken r at a time represent the number of arrangements of n elements taken n at a time, using factorial notation determine the number of permutations of n elements taken n at a time where some elements are not distinct Use the flowchart to help you throughout this lesson. Click on the image to enlarge.

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Explore the properties of some common three-dimensional shapes with this printable mini-book. 3D Shape Properties… Explained! Let’s face it… primary-aged children LOVE little books! We’ve capitalized on this fact by creating an informative and age-appropriate mini-book to deepen your students’ knowledge and understanding of some common 3D figures and their properties. By engaging with this resource, students will learn about the following three-dimensional shapes: - Rectangular prism - Triangular prism For each object, students are required to: - Read about the object’s properties. - Draw the object. - Record the number of faces, edges and vertices, or the number of flat and curved surfaces. How to Create This 3D Shapes Mini-Book This resource contains nine pages. Each page includes two mini-book pages (18 pages in total). To assemble the mini-book, follow these simple steps. - Print out the resource. Create copies as required. - Cut each page along the dotted line. - Compile the pages in order. - Staple the pages along the left-side margin to create a booklet. - Distribute to the students. A Note About Cones and Cylinders Within this resource, you will notice the following properties are attributed to cones and cylinders: - Cones – 1 flat surface, 1 curved surface - Cylinders – 2 flat surfaces, 1 curved surface In geometry, the following definitions apply to faces, edges and vertices: - Face – A flat surface with straight edges. - Edge – A straight line formed by two faces meeting. - Vertex – The point where two or more edges meet. According to these definitions, a cone has no faces, edges or vertices. It has one flat surface, one curved surface and one apex. Similarly, according to these definitions, a cylinder has no faces, edges or vertices. It has two flat surfaces and one curved surface. Should you wish to adapt these definitions, please download the editable Google Slides version of this resource. Easily Prepare This Resource for Your Students Use the dropdown icon on the Download button to choose between the easy-print PDF or the editable Google Slides version of this resource. This resource was created by Jodi Chubb, a teacher in Pennsylvania and a Teach Starter collaborator. Click below for more great resources for teaching 3D shapes to your students! Draw, name, and describe the features of 3D figures with this profiling template. Practice identifying 3D shapes and their properties in multiple ways with this engaging interactive activity. Learn the names and properties of some common 3D shapes with this set of classroom anchor charts.

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thermal conductivity, the ability of a substance to conduct heat or move heat from one location to another without the movement of the material conducting the heat. Thermal conductivity is measured in watts per meterkelvin (W/mK). For example, solid aluminum has a thermal conductivity of 237 W/mK at –73 °C (–99 °F), 236 W/mK at 0 °C (32 °F), and 232 W/mK at 327 °C (621 °F). Thermal conductivity of a material changes with temperature and can be related to changes in pressure, depending on the state of the material. In physics, thermal conductivity is given the symbol k or λ. It represents one of three methods by which heat can be transferred from one location to another, the other two being convection and radiation. Fourier’s law of heat conduction gives the rate at which heat is transferred through thermal conductivity: q = –k∇T, where q is local heat flux density, and ∇T is the temperature gradient. When heat is conducted through a solid, heat moves through molecular or atomic agitation and contact between particles. Heat transfer is not the result of atoms or molecules moving through the solid. In a solid, heat moves along a difference in temperature (called a temperature gradient) from an area of high temperature and thus high particle agitation to an area of low temperature and thus low particle agitation. This transfer of heat energy continues until all the material comprising the solid is at thermal equilibrium, meaning the temperature throughout the material is the same. The time needed for this to occur depends on several factors, including the magnitude of the temperature difference within the material and the thermal characteristics of the material itself. These characteristics include the material’s atomic or molecular composition and the distance, known as the path length, through which the heat must move. When the conducting material is a liquid or a gas, heat moves through particle agitation as well as through movement of the atoms or molecules themselves. Thermal conduction occurs fastest in a solid and slowest in a gas. When matter is in the gas phase, particles have larger distances between them and so collide less often. These collisions transfer thermal energy, so fewer collisions lead to a lower rate of heat conduction. Examples of thermal conductivity When cooks prepare food, they often use metal frying pans. As a pan heats on a stovetop, thermal energy from the stovetop is transferred to the metal on the bottom of the pan. This energy is then conducted throughout the pan, ultimately cooking the food. However, over time, the heat will also conduct to the handle of the pan. Therefore, frying pan manufacturers will often carefully select a material for the handle of a pan that is a poor conductor of heat so that cooks will not be in danger of burning their hands. Thermal touch, or how the body senses temperature when touching a hot or cold object, also follows the principles of thermal conductivity. When a person touches an object, the temperatures of the object and skin change depending on both their properties and their initial temperatures. Are you a student? Get Britannica Premium for only $24.95 - a 67% discount!

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By the end of this lesson, students will be able to explain why it’s important to follow the rules in class. - Powerpoint or other visual aid - Whiteboard or marker board 1. Introduction (5 minutes) - Welcome all students and explain the lesson objective, that students will be learning about why it’s important to follow the rules in class. - Introduce yourself and other educators who may be present in the classroom. 2. Review Rules (10 minutes) - Present a visual aid of the classroom rules that have been set by the school and/or classroom teacher, such as raising your hand when you want to speak, not talking while the teacher is speaking, cleaning up after class, and respecting others’ opinions. - Ask students why they think these rules have been put in place. - Allow time for the students to discuss their understanding and explain to them why the rules have been set (e.g. the rules keep the classroom environment safe and respectful). 3. Role Playing (15 minutes) - Explain to students that they will be role playing different situations that occur in class and why it’s important to follow the rules in each situation. - Divide the students into different groups and give each group a scenario (e.g. A student asks an inappropriate question or a student finishes their work early). - Ask each group to come up with two different endings for the scenario (one ending where the rules are followed, and one ending where the rules are not followed). - Encourage students to think critically about why the ending might be different depending on whether the rules are followed or not. 4. Discussion (10 minutes) - Ask each group to share their scenarios and endings with the class. - Discuss why following the rules is important in each situation. - Ask the students to explain what would happen if they didn’t follow the rules. 5. Wrap-up (5 minutes) - Summarise to the students what was learnt in the lesson. - Ask if there are any questions and answer them. - Thank the students for participating and let them know that they can continue to refer back to the rules in the classroom.

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In English, we encounter adjectives on a regular basis as they play a crucial role in providing more intricate details to our sentences. They function to describe or modify nouns and pronouns. But did you know adjectives can also function as nouns in certain contexts? Yes! Adjectives can do more than just decorate your prose. They can actually transform into subjects, objects, and complements. Understanding how adjectives function as nouns can elevate both your writing and comprehension, especially in more advanced contexts. In this tutorial, we will delve deep into this aspect of English grammar and see how adjectives function as nouns. Before diving into how adjectives function as nouns, it's crucial to understand what an adjective is. An adjective is a word or phrase that modifies or describes a noun or a pronoun. It gives more information about the quality, quantity, or size of the noun. For instance, in the sentence, "She has a big house," the adjective "big" describes the noun "house." Examples of Adjectives Adjectives functioning as Nouns In English, adjectives can sometimes be used as nouns. This usually happens when an adjective is used to refer to a group of people with a certain quality. Although it may seem unusual to some, this is quite common in English language usage. When an adjective is used in this way, it is often referred to as a substantive adjective or an adjectival noun. Examples of Adjectives acting as Nouns Let's take a look at some examples: - The rich should help the poor. (Here, "rich" and "poor" are adjectives representing two different groups of people, and hence they are functioning as nouns.) - Young and old alike will enjoy this film. (In this sentence, "young" and "old" are acting as nouns, representing different age groups.) Rules for using Adjectives as Nouns While using adjectives as nouns, there are certain rules that need to be followed: 1. Use of Definite Articles When an adjective is used as a noun in English, it is usually preceded by the definite article 'the'. It signifies that the adjective is being used to refer to a specific group of people or things. 2. Context Matters To understand whether an adjective is being used as a noun, the context of the sentence is crucial. Without the context, it can be difficult to distinguish whether an adjective is acting as a noun or not. Why use Adjectives as Nouns? Adjectives are used as nouns in English for a variety of reasons: 1. To Provide Short and Concise Information Using an adjective as a noun can help to make communication more concise and clear. For instance, instead of saying "People who are blind should be helped," we can say "The blind should be helped." This is shorter and more direct. 2. To Refer to a Group of People with a Similar Quality Adjectives can be used effectively as nouns to describe a group of people who share a certain characteristic, such as "the elderly" or "the unemployed." Common Mistakes to Avoid There are a couple of mistakes people often make while using adjectives as nouns: 1. Forgetting the Definite Article One common mistake is forgetting to use the definite article 'the'. Since the adjective is being used as a noun, 'the' is necessary to refer to the specific group the adjective is representing. 2. Misunderstanding due to Lack of Context Another mistake is using an adjective as a noun without providing sufficient context. Without enough context, it can be quite confusing to comprehend the meaning of the sentence. The use of adjectives as nouns, though standard in English, can be relatively complex to grasp as it goes beyond the conventional use of adjectives. However, with practice and proper understanding of the rules and reasons for substantives, your mastery over the English language can be significantly broadened. In conclusion, be open to stepping out of the conventional grammatical zones and venturing into areas such as adjectives serving as nouns. It's fascinating to observe how the English language can bend, stretch, and alter traditional grammar norms to suit communication needs. Happy learning!

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Reading intervention is instruction designed to meet a student’s specific learning needs in addition to grade level core reading instruction. It is often part of a school’s Response to Intervention or Multi-Tiered System of Support process. The best way to improve reading skills is by understanding HOW students learn. That means training teachers in evidence-based practices, using frequent assessments and ensuring that curriculums are backed by research. The ability to understand the meaning of text is fundamental for all learning. Comprehension is different from decoding, as it involves constructing mental representations of the text and connecting them with prior knowledge to fill in gaps in understanding. It also requires understanding text structures, identifying relevant text clues and making inferences to make sense of the text (Stahl, 2020). Students’ comprehension skills are impacted by many variables. These include background knowledge, vocabulary level, cognitive abilities and motivation. Additionally, the complexity and unfamiliarity of text can inhibit or enhance comprehension. Teaching students reading comprehension strategies has been found to be an effective method for improving their comprehension. Reciprocal teaching approaches have proven successful, as they require students and teachers to engage in discussion of the text in a “cognitive apprenticeship” model. Teaching strategies that involve self-questioning, constructing mental representations to integrate information from the text and identifying text consistencies have been shown to be particularly effective. Phonics is an approach to teaching reading that emphasizes letter-sound relationships. It provides a foundation for decoding unfamiliar words, enhancing their spelling and word recognition skills. It is an essential skill for students who are struggling with reading because it allows them to break words into syllables and pronounce them correctly. It also helps them understand the rules of English grammar, such as the difference between long and short vowels and their variations. The goal is for students to rely on phonics to read the majority of words they encounter in their everyday life. This enables them to quickly gain fluency and comprehension. To help children build phonological awareness and sound-letter correspondence, teachers should use a variety of teaching methods. A comprehensive phonics program should include the alphabetic principle, phonemic awareness and strategies for blending and segmenting sounds. The program should also address vowel teams and variant vowels to help students learn how to read more complex words. A person’s vocabulary is the group of words that he or she knows and uses in speech and writing. It is also referred to as word stock, lexicon, or lexis. Vocabulary is an important aspect of reading comprehension. It is important for students to build their vocabularies by increasing the number of words they encounter in reading and in speaking. This will help them understand the meaning of new words and will improve their comprehension skills. Vocabulary instruction should be meaningful and not simply focused on providing a list of words to memorize. Teachers should scour their reading materials for unfamiliar words and provide contexts to allow learners to discover them. Moreover, teaching academic Tier 2 vocabulary provides learners with a broader range of meanings than basic or domain specific words. Research shows that a person’s ability to comprehend depends on his or her vocabulary. A strong vocabulary allows people to visualize stories, anticipate events in a story, and understand jokes. Reading fluency helps students build the bridge between word recognition and comprehension. Fluent readers read accurately, smoothly and with expression, and they group words rapidly to gain meaning from the text. Non-fluent readers struggle with decoding skills and sound choppy when they read. Teaching strategies for fluency can include repeated oral reading, especially with a model, rhyming or rhythmic texts, and phrasing and expression instruction (e.g., intonation, volume and smoothness). Prosody can also be taught through a focus on phrase boundaries and pauses to help students who do not pick up expression intrinsically. It is important to track student progress in fluency using a running record or chart to show the student how much they have improved. This will help boost their motivation and give them the sense of achievement they need. You can also use a partner reading strategy where a fluent reader is paired with a struggling student to model fluent reading.

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Jason and his friends can not rely solely on the expression of their feelings to ensure effective social interactions. For every expression of emotion, another person or group must interpret the feelings and emotions being communicated. The interpretation of another person’s feelings is complex. In order to develop a valid sense of another person’s emotions, the listener must devote attention to actively listening, and also, review his/her memory for similar social situations. Key neurodevelopmental functions underlying the accurate interpretation of emotions include attending to and recognizing the type of words being used, and how the words are being said, identifying and labeling the feelings of the speaker, and waiting for more information to validate the listener’s interpretation of the speaker’s emotions. Here are some strategies to help students develop their ability to interpret the feelings of others. - Use an advance organizer to focus student attention on how the targeted skill of understanding the feelings of others fits into the context of daily social settings, friendships, etc. - Build students’ ability to interpret the feelings of others by having them practice: - inhibiting their initial responses or reactions and taking time to think about the situation, such as during a role-play activity - taking the perspective of others in an attempt to understand their feelings, such as in a story or role-play - reading the non-verbal cues in an interaction that help reveal a person’s feelings, such as in a movie or role-play - understanding the image another person is trying to develop and project as a cue to his/her feelings, such as in a story or movie

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- Core Idea 1: Number Properties - Understand numbers, ways of representing numbers, relationships among numbers, and number systems. - Understand whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers. - Understand the relative magnitude of whole numbers and the concepts of sequences, quantity, and the relative position of numbers. - Demonstrate an understanding of the base-ten number system and place value concepts. - Represent commonly used fractions such as 1/2, 1/3, and 1/4 in a variety of ways. - Core Idea 2: Number Operations - Understand the meanings of operations and how they relate to each other, make reasonable estimates, and compute fluently. - Demonstrate fluency in adding and subtracting whole numbers. - Use strategies to estimate and judge the reasonableness of results. - Understand situations that entail multiplication and division such as equal groupings of objects and equal sharing. - Core Idea 3: Patterns, Functions, and Algebra - Understand patterns and use mathematical models to represent and understand qualitative and quantitative relationships. - Describe, extend, and create patterns of sound, shape, and number and translate from one representation to another. - Describe, extend, and create growing as well as repeating patterns. - Compare principles and properties of operations, such as commutativity, between addition and subtraction. - Use concrete, pictorial, and verbal representations to develop an understanding of symbolic notations. - Describe change quantitatively such as a student's growing two inches in one year. - Core Idea 4: Geometry and Measurement - Recognize and use characteristics, properties, and relationships of two- and three-dimensional geometric shapes and apply appropriate techniques to determine measurements. - Describe and classify two- and three-dimensional shapes according to their attributes and/or parts of their shapes - Develop an understanding of how shapes can be put together or taken apart to form other shapes. - Develop an understanding of line symmetry. - Understand how to measure using non-standard and standard units. - Select an appropriate unit and tool for the attribute being measured (length, volume, weight, area, time). - Use number concepts in geometric contexts. - Core Idea 5: Data Analysis - Collect, organize, display, and interpret data about themselves and their surroundings. - Write a survey question for a given situation. - Represent and interpret data using pictographs, bar graphs, tally charts, Venn diagrams, and other representations. - Describe and compare data using qualitative and quantitative measures. - Represent the same data in more than one way.

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Lesson Plans and Worksheets Browse by Subject Thermodynamics Teacher Resources Find teacher approved Thermodynamics educational resource ideas and activities More than a week's worth of investigation is provided in this source. Physical science stars experiment to describe specific heat, conduction, convection, and radiation. They also discover the relationship between mechanical and thermal energy. These activities are all illuminating. You do not need to use all 12 to thoroughly introduce learners to thermodynamics concepts, but each of them is sure to ignite understanding! This is a review of how advanced chemistry learners handle thermodynamics equations and calculations. Charts and graphs are included for them to read in addition to solving related problems. You will find this resource useful as a review homework or preparation for a unit quiz. Students examine the efficiency of energy conversion as a consequence of the laws of thermodynamics by measuring the power radiated by a light bulb. Students compare the electric power input and the power radiated in order to calculate the efficiency with which the bulb converts electric energy to light. A brief chemistry activity provides two different example problems. When learners complete the activity, they practice calculating the specific heat of a metal and the enthalpy for a reaction. Teach your advanced chemists how to work with thermodynamic concepts with these example problems.

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Neutrons are neutrally charged subatomic particles that, along with protons, make up the nucleus of an atom. Neutrons were first discovered in 1932 by James Chadwick as an uncharged particle approximately the size of a proton. The number of neutrons in an atom is equal to the atomic mass minus the atomic number (number of protons). For a given element, different isotopes of that element will have different numbers of neutrons. For example, carbon-12 and carbon-14 are both atomic number 6, but they have 6 and 8 neutrons, respectively. When an atom has too many neutrons, it becomes radioactive and will shed radiation or particles over time. Design a lab to measure the distance an accelerated object moves over time. Use equal time intervals so that you can plot velocity over time as well as dis-tance. A pulley at the edge of a table with a mass attached is a good way to achieve uniform acceleration. Suggested materials include a motion detector, CBL, lab cart, string, pulley, C-clamp, and masses. Generate distance-time and velocity-time graphs using different masses on the pulley. How does the change in mass affect your graphs?• The reaction 2NO2(g) + Cl2(g) <==> 2NO2Cl(G) has an equilibrium constant equal to 1.567x10^7 at 25Celsius. A flask contains .100M NO2(g), .0500 M Cl2(g), and .150 M NO2Cl(g), which is allowed to react until the system comes to equilibrium. Determine the partial pressure (in atm) of each gas at equilibrium.• Join Chegg Study and get: Guided textbook solutions created by Chegg experts Learn from step-by-step solutions for 9,000 textbooks in Math, Science, Engineering, Business and more 24/7 Study Help Answers in a pinch from experts and subject enthusiasts all semester long

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Students take a quiz that involves earning income and paying a tax. Through this activity, they generate data that they use to create a table, a graph, and to build equations that represent relationships between quantities. Students scale and label axes as they create graphs of relationships between income and tax. Tables and graphs of data are then used by the students to construct equations representing examples of relationships between income, tax, and average tax ratio. Students explore the graphs to draw conclusions about the impact of different tax structures on families with different incomes. Note: Students should have prior knowledge of graphing linear functions for this lesson. What determines a person's salary? Why do professional athletes make so much money? People who work as firefighters, police officers or teachers are clearly more important to our society, yet they make much less money than jocks. What explains this? Each of us seek to make wise investment decisions that will make our money grow. Unfortunately, we cannot predict the future, but the past can give us a window to understanding the risks and rewards of investing in the stock market. This lesson will track the history of a Dow Jones 30 stock and enable to student to calculate the return on his investment. The following lessons come from the Council for Economic Education's library of publications. Clicking the publication title or image will take you to the Council for Economic Education Store for more detailed information. This publication helps students analyze energy and environment issues from an economics perspective. 6 out of 10 lessons from this publication relate to this EconEdLink lesson. Use this DVD program to show students how to live healthy, wealthy and risk-free. 3 out of 12 lessons from this publication relate to this EconEdLink lesson. Created as a supplement to existing middle school world geography and world history courses, the 5 units in this guide introduce students to the basics of global trade. 2 out of 7 lessons from this publication relate to this EconEdLink lesson.

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This preview shows pages 1–3. Sign up to view the full content. This preview has intentionally blurred sections. Sign up to view the full version.View Full Document Unformatted text preview: Section 9.1 The Square Root Function 869 Version: Fall 2007 9.1 The Square Root Function In this section we turn our attention to the square root function, the function defined by the equation f ( x ) = √ x. (1) We begin the section by drawing the graph of the function, then we address the domain and range. After that, we’ll investigate a number of different transformations of the function. The Graph of the Square Root Function Let’s create a table of points that satisfy the equation of the function, then plot the points from the table on a Cartesian coordinate system on graph paper. We’ll continue creating and plotting points until we are convinced of the eventual shape of the graph. We know we cannot take the square root of a negative number. Therefore, we don’t want to put any negative x-values in our table. To further simplify our computations, let’s use numbers whose square root is easily calculated. This brings to mind perfect squares such as 0, 1, 4, 9, and so on. We’ve placed these numbers as x-values in the table in Figure 1 (b), then calculated the square root of each. In Figure 1 (a), you see each of the points from the table plotted as a solid dot. If we continue to add points to the table, plot them, the graph will eventually fill in and take the shape of the solid curve shown in Figure 1 (c). x 10 y 10 x f ( x ) = √ x 1 1 4 2 9 3 x 10 y 10 f (a) (b) (c) Figure 1. Creating the graph of f ( x ) = √ x . The point plotting approach used to draw the graph of f ( x ) = √ x in Figure 1 is a tested and familiar procedure. However, a more sophisticated approach involves the theory of inverses developed in the previous chapter. In a sense, taking the square root is the “inverse” of squaring. Well, not quite, as the squaring function f ( x ) = x 2 in Figure 2 (a) fails the horizontal line test and is not one-to-one. However, if we limit the domain of the squaring function, then the graph of f ( x ) = x 2 in Figure 2 (b), where x ≥ 0, does pass the horizontal line test and is Copyrighted material. See: http://msenux.redwoods.edu/IntAlgText/ 1 870 Chapter 9 Radical Functions Version: Fall 2007 one-to-one. Therefore, the graph of f ( x ) = x 2 , x ≥ 0, has an inverse, and the graph of its inverse is found by reflecting the graph of f ( x ) = x 2 , x ≥ 0, across the line y = x (see Figure 2 (c)). x 10 y 10 f x 10 y 10 f x 10 y 10 f f − 1 y = x (a) f ( x ) = x 2 . (b) f ( x ) = x 2 , x ≥ 0. (c) Reflecting the graph in (b) across the line y = x produces the graph of f − 1 ( x ) = √ x . Figure 2. Sketching the inverse of f ( x ) = x 2 , x ≥ 0. To find the equation of the inverse, recall that the procedure requires that we switch the roles of x and y , then solve the resulting equation for y . Thus, first write f ( x ) = x 2 , x ≥ 0, in the form y = x 2 , x ≥ .... View Full Document

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Common Nouns and Proper Nouns In this noun worksheet, students read about common and proper nouns. They read a paragraph and circle the common nouns and underline the proper nouns. 7 Views 94 Downloads Using Nouns (Grade 3) Teach your class how to identify the people, places, and things that they see in the world around them with this two-part grammar activity. After first circling all of the nouns in a collection of 25 words, children then must use the... 2nd - 4th English Language Arts CCSS: Adaptable What's In a Noun: Grammar and Usage Nine lessons in a grammar and usage unit provide endless opportunities for drill and practice. Topics include the four types of sentences, subject and predicates, nouns, verbs, adjectives, pronouns, adverbs and prepositions, conjunctions... 5th - 8th English Language Arts Daily Warm-Ups: Grammar and Usage If grammar practice is anywhere in your curriculum, you must check out an extensive collection of warm-up activities for language arts! Each page focuses on a different concept, from parts of speech to verbals, and provides review... 3rd - 6th English Language Arts CCSS: Adaptable

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Follow Me on FACEBOOK!! The purpose of this activity is to help students develop a conceptual understanding of equality. Students must understand that the equal sign does not express the “answer,” but rather indicates that two expressions have the same value. TEKS 4.(5)A Algebraic reasoning. The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to: represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with a letter standing for the unknown quantity; 4.(4) H Number and operations. The student applies mathematical process standards to develop and use strategies and methods for whole number computations and decimal sums and differences in order to solve problems with efficiency and accuracy. The student is expected to: solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

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Mathematical process standards and best practices tell us that students need to be communicating about math, defending and justifying their answers and explaining their thinking. Whether we call them Math Talks, Number talks, or Problems of the Day a whole group time to think about math, talk about math, and learn from mistakes is a critical part of the math day. At the beginning of the year, establish procedures for math talks by telling kids you our group is looking for all answers and thoughts as we learn from mistakes just as well as we learn from accuracy (sometimes we even learn more from mistakes!) Model and discuss appropriate comments and responses for open mathematical discussions. Also provide sentence stems to help you students phrase their comments for mathematical debate. There are lots of great resources for these on TpT. Then, at the beginning of class 2-3 times per week post a Think and Thumbs Up problem for your class. You can project it on a smart board or under a document camera. Without comment from other classmates, collect student answers and record them in the “answers” box. Let students think again about which answers make the most sense to them. Then open the floor for debate and sharing of mathematical thinking. As students come to consensus on patterns or rules that could be used, them in the “patterns and notices” box. Let the students lead the discussion where it needs to go for them. Try to avoid guiding them to see math the way you see it and let them discover the truths of math through their own struggle, discussions, and light-bulb moments. This set includes resources for a full year with topics including multiplication, division, addition, subtraction, patterns, algebraic thinking, fractions, geometry, measurement, time, money, and place value. The problems are grouped by topic and come with an answer key including some ideas for where the conversations might go. Looking for Math Games? Find 4 in Forty-Mathematical Operations and Problem Solving Hit the Target-A Multiplication Facts Game Place it or Pass It-A Place Value Game Multiplication Card Games Mega Pack

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Counting Blocks 2 In this mathematics worksheet, students solve various problems by counting the blocks illustrated for each problem. There are six problems to solve on the sheet. 3 Views 1 Download Working with 10s and 1s, Part 2 Practice place value by visualizing 10s and 1s. First graders count the cubes in each place, then write the total number at the bottom. In one particularly helpful section, they draw the cubes that will add up to a given number. Bring in... K - 2nd Math CCSS: Designed

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A collection of esl, efl downloadable, printable worksheets, practice exercises and activities to teach about vowel sounds. What about long vowels and diphthongs a long vowel sounds kind of like saying the name of the letter on the vowel sounds, don't worry the exercises below will . Home » unit 3 » stage 1: han-gǔl graphs and syllables i » graphing han-gǔl consonants and vowels graphs » consonants and vowels writing exercises consonants and vowels writing exercises print out the following pdf files to practice your writing. Vowel worksheets short and long vowel worksheets what is a short and long vowel a vowel is a speech sound and a type of letter of the alphabet the vowels in the english language are a,e,i,o,u. English exercises presents our new interactive self-correcting worksheets and workbooks english sounds (1/ 2 - vowels and diphthongs) mada_1 long and short . Esl exercise: short and long vowel sounds [english pronunciation exercise] now that you learned the 7 pronunciation guidelines and practiced the last esl activity . Vowel sounds questions for your custom printable tests and worksheets in a hurry grade 1 long vowels skip planted a in his garden sead sede . Short vowel u worksheets for kindergarten phonics worksheet sounds printable,short u sound worksheet vowels printable long and vowel sounds exercises pdf phonics worksheets for kindergarten review,short and long vowel sounds worksheet pdf sound a e teaching worksheets for math i phonics first grade,short vowel sound practice worksheets phonics sheets word family homework and classwork . Focus on the long and short i vowel sounds with these worksheets long o, short o this set of phonics worksheets teaches students about the long and short o sound. Use this 'vowel sounds: long and short u' printable worksheet in the classroom or at home your students will love this 'vowel sounds: long and short u' booklets to illustrate for long and short u sounds, sorting worksheets, complete the sentence exercises, a word search, and much more. Short and long vowels : phonics : first grade english language arts worksheets below, you will find a wide range of our printable worksheets in chapter short and long vowels of section phonics these worksheets are appropriate for first grade english language arts . Long vowel worksheets : phonics long vowel sound writting worksheets for kindergarden and 1st grade. Our long vowel listening game pages are the perfect way to get kids listening for the long vowel sounds they hear in words it can help by teaching kids long vowel patterns by word families the -ake family is one of my favorite word families to start with because you can spell so many words with it. This printable long vowel o words worksheet is perfect for kids that learning to recognize the long vowel o sound this worksheet lists 24 words and asks kids to circle the words that contain the long vowel o sound. Within this collection of 81 free phonics worksheets, students practice learning vowels, beginning consonants, ending consonants and plurals, beginning blends, ending blends, consonant digraphs, long vowel sounds, r-controlled vowels, diphthongs, ph and gh, silent consonants, and more. Exercises: compound vowels the page you're reading right now is an exercise page exercise pages contain exercises that allow you to practice your sanskrit skills and make sure that you've understood the material in the lesson. Ela reading - vowel sounds worksheets i abcteach provides over 49,000 worksheets page 1. Practice materials for vowel contrast (ame) this material can be used as additional phonetic exercises for practicing contrasting vowels in short words and phrases. Vowels: short or long a sound words 1 page worksheet downloadfree worksheet pdf digital download 1 page grade preschool, kindergarten long vowels sound . Long and short vowels lessons 1 - 12 what: there are five primary letters that are vowels: a, e, i, o, u each vowel can make a long sound or a short sound the long vowel sound is the same sound as the name of the letter. Second grade level 1 reading activities: practice the vowel digraph ‘oa’ which has the long o sound oa vowel digraph audio cards. Practise the short vowel sounds of british english check out wwwtefltalknet for more teaching material. This is the first long vowel programme in our series of 45 pronunciation videos that explore the sounds of english.

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PDF (Acrobat) Document File Be sure that you have an application to open this file type before downloading and/or purchasing. This activity sheet, containing twenty exercises, has students using real formulas from mathematics and science as the literal equations. In each exercise students are told which variable they need to solve for. Of the twenty exercises, five have been starred. When students have solved these five literal equations for the new variable, the students are asked to write a sentence explaining what this new formula tells them about the relationship of the other variables in the formula. Common formulas include • the area of a triangle • the area of a circle • the volume of a cone • the work equation • the area of a trapezoid • the formula for acceleration • the formula for the total angle measure in a regular polygon • the Pythagorean Theorem • the surface area of a cone • the surface area of sphere • the volume of a sphere • the surface area of a cube • the formula for the measure of one angle of a regular polygon • the perimeter of a rectangle • the formula for the conversion between Fahrenheit and Centigrade • the formula for the surface area of a rectangular prism • the formula for the height of a projectile • the formula for the volume of a rectangular prism A set of solutions for all exercises is included.

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PDF (Acrobat) Document File Be sure that you have an application to open this file type before downloading and/or purchasing. During this "How To' Unit, students will explore How To (Procedural Texts) of topics of interest. Students will be given the opportunity to explore the concepts covered in the lesson through a variety of learning styles. What is a “How-To” Book? - teaches how to do something with words and/or pictures. - has steps or directions in order. - tells what is needed to make something. - usually short books. Questions: While students make observation of different procedural text. 1. What is your book about? 2. What is the first step in your book? 3. What is your book showing us? 4. How many steps are shown in your book? 5. What are the pictures showing/ telling you? 6. What is the main topic of your book?

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Lesson Plan Template: General Lesson Plan Learning Objectives: What should students know and be able to do as a result of this lesson? Students should be able to: - list and explain the various physical properties used to identify minerals such as the hardness, color, luster, cleavage, and streak color of specific minerals (quartz, feldspar, biotite mica, calcite, pyrite, graphite, and talc). - determine the relative hardness of a mineral. - identify the color of a mineral is a physical property. - identify the luster of a mineral as metallic or nonmetallic. - identify the streak color of a mineral. - identify the presence or absence of cleavage in a mineral. Prior Knowledge: What prior knowledge should students have for this lesson? Students should have some background knowledge about the physical properties that they will be testing in this lab activity. Prior to the lab, have students review the material using resources on hand or refer students to this resource online: http://www.kidsloverocks.com/html/physical_properties_of_mineral.html Before students begin lab activity, they should be able to: - Define the word "mineral." - Explain the physical properties used to identify minerals such as hardness, color, luster, cleavage, and streak color. - Explain that hardness is how easily a mineral can be scratched. - Explain that luster describes how the surface of the mineral reflects light. - Define streak color as the color of a mineral's powder. - Define cleavage as how a mineral breaks along flat planes. - Explain that the color of the mineral is the color they see. Guiding Questions: What are the guiding questions for this lesson? - How can the physical properties of a mineral be determined and used to identify it? - How can you determine the hardness of a mineral? - How do colors compare across mineral samples? - How can you determine the actual color of a mineral, especially if it is tarnished or oxidized? - How can you classify minerals as metallic or non-metallic using physical properties? - Do all minerals break the same way? Teaching Phase: How will the teacher present the concept or skill to students? See attached PowerPoint as a guide for teaching this lesson. Begin the lesson with a brief review: partners will take turns verbally identifying the properties of minerals. These should include the characteristics of a mineral (naturally occurring, solid, inorganic, crystalline, a specific chemical structure, mostly pure) and the physical properties including color, streak color, luster, cleavage, and hardness. Cooperative Learning Activity for Review: Pass out the question cards to students and explain the rules. Students move around the room, finding a random partner and asking them the question on their card. After both partners have asked and answered the questions, students trade cards and find a new random partner. Students will be given 3 minutes for this task. In order to monitor student understanding circulate and listen to students as they answer the questions or coach if needed. Bring students back to seats. The teacher states the target: "Our target today is to compare and contrast minerals by their physical properties of hardness, color, luster, cleavage, and streak color. Today we are going to practice our knowledge of hardness, color, luster, cleavage, and streak color to compare a set of minerals. You will be working with your shoulder partner to complete a lab where you will test the relative hardness and streak, describe the color and luster, and determine if cleavage is present in the sample." Review the lab instructions with the class. Students will be working with a partner (recommended) or in triads. Groups of 4 are not recommended for this activity. Note: Place students with shoulder partners (or in triads if necessary). Arrange partners so that pairs have mixed ability. Higher-level students should be working with a low-medium partner, and a high-medium student should be working with a lower-level student. Pass out lab sheets and place materials for each pair/group on the tables. Materials include: set of minerals (quartz, feldspar, biotite mica, calcite, pyrite, graphite, and talc), nail, penny, hand lens, flashlight, pencil, lab sheet, tray, moist paper towel, white streak plate, black streak plate - Organizational tip: place each type of mineral sample in numbered bags; this allows students across groups to compare the same mineral type. Stress to students that they must keep the minerals in their numbered bags for identification later on. Have students quickly do a materials check to ensure that all materials are present. Review lab safety rules: Review the components of the lab and safety information. (Follow the Lab Safety Rules as outlined by the State of Florida: http://fldoe.org/academics/standards/subject-areas/math-science/science/safety-in-science.stml). - Keep mineral samples away from eyes and mouth. - Use caution when handling the iron nails and streak plates. Mineral samples should be held carefully. - Do not throw or toss items to anyone. Hand items to your partner. - If something breaks, inform the teacher immediately! - Wear eye protection. - When finished, wash hands with soap and water. Explain to students: There are five activities and one optional extension activity in this lab and a time limit will be given for each component. If you need help, students should first ask their partners or group members, then ask table groups near you, then ask the teacher. Please raise your hand to signify that you need assistance, but keep working until the teacher is able to reach you. Guided Practice: What activities or exercises will the students complete with teacher guidance? Have students work through the properties of minerals lab sheet with teacher guidance for the first activity: Activity 1: Hardness – Students will test their mineral samples for hardness. - Have students read the problem and make a prediction. - Students retrieve the penny, nail, and Mohs hardness scale from the lab kit. - Guide students to choose the first mineral sample. - Each student will test for hardness. - Remind students to use their fingernail to scratch the surface of the mineral. Determine if the fingernail leaves a mark or not. If the fingernail does not leave a scratch, try the penny. If the penny does not scratch the mineral, try the iron nail. If the iron nail does not scratch the mineral sample, the hardness is above 6. Stop testing once a tool leaves a scratch on the mineral. Some minerals may be too hard to scratch with the tools provided for this lab. - Students record their findings on their lab sheet. (Circulate around the room and make sure that all students fill in their own recording sheet.) - Work with students to complete the hardness test for all 7 minerals. - Students draw a conclusion from their findings. Which mineral was hardest? Which mineral was softest? Place them in order from hardness level 1 to the hardest mineral. (Circulate and monitor that students are completing the prediction question and the conclusion statement.) Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson? Student groups continue to work on the lab activities. Circulate throughout the room as they work. Students need to complete the prediction question before beginning each activity. When they have completed each activity, students need to answer the conclusion statement. Students should be talking with their partner(s) and discussing their ideas. Activity 2: Students describe each mineral's color. Students read the problem and make a prediction. Students will need the mineral set and a hands lens from the lab kit. Student use the hand lens to observe the mineral sample and describe the colors they see. Record the data on the lab sheet. Ask students to draw a conclusion: Can you identify the mineral based only on its color? Activity 3: Streak test: Students will describe each mineral's streak color. Have students read the problem and make a prediction. Students will need the mineral set, hand lens, white streak plate, black streak plate, and a moist paper towel. Students perform the streak test using both color plates. Instruct students to carefully and gently draw the mineral once across the streak plate. Using the hand lens, look at the powdered streak left on the plate. Note that some of the mineral streaks will not show up on the white streak plate. Students should use both the white and black streak plates. Determine the color of the powdered streak on the plate. Record this color on their lab data sheet. Answer the conclusion question, "How does the streak color compare to the color of the mineral?" Activity 4: Luster: Students will describe each mineral's luster as metallic or nonmetallic. Students will need the mineral set and a flashlight. Students shine the flashlight on the rock to determine if the mineral reflects light like a metal or is nonmetallic. Answer the conclusion question, "What do you think luster tells you about a mineral?" Activity 5: Cleavage: Students will determine if the mineral sample has cleavage. Have the students read the problem and make a prediction. Students will need the mineral set and hand lens. Students will observe each mineral and determine if the mineral has been broken in flat edges or planes. Add the data for each sample to the data sheet. Ask students to draw a conclusion: Do all minerals break the same way? Closure: How will the teacher assist students in organizing the knowledge gained in the lesson? Activity Reflection: Students choose two minerals and compare them across their properties. What do you notice? How are they the same? How are they different? (Consider using a Double Bubble Thinking Map or Venn Diagram.) What do you think this tells you about the minerals' compositions? Choose one physical property and look across the collection of samples. What conclusions can you draw about the physical properties of minerals? Wrap Up Activity: Move it and Compare! (Students will move, find a new partner, and discuss one of the two reflection questions.) - Students stand up, push their chairs in. - Hold their hand up in the air. - Walk quietly around the room. - Find a new partner and high-five. - Stand quietly together until all partners have been found. - Partner A discusses one of the reflection questions for 1 minute. Partner B listens quietly. - Partner B thanks Partner A. - Partner B discusses one of the reflection questions for 1 minute. Partner A listens quietly. - Partner A thanks Partner B. - Return to seats quietly. Students should complete the exit ticket out the door. Dennis cannot scratch a mineral sample with his fingernail, but he observes that he can scratch the mineral sample with a piece of metal. What physical property of the mineral sample is Dennis investigating? (FCAT 2.0 2012 Science Test Item Specifications Version 2, p. 47) Student Data Sheets will provide formative assessment data for the teacher to check while circulating. The teacher can spot check by asking questions to groups. The teacher can correct any misconceptions at this time or to have students clarify their explanations. Feedback to Students Students will compare their data with standard data to make sure they are on the right track. Students will be able to self evaluate however the teacher should also be facilitating and assisting any students that are off track. The teacher will circulate and provide targeted specific feedback to students on the process and the data collection.

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Access thousands of brilliant resources to help your child be the best they can be. Brush up on your own literacy skills, clear up homework confusion and understand exactly what your child is learning at school by reading our basic definitions with links to more detailed explanations, teachers' tips and examples. You'll find basic definitions of important primary-school literacy terms below. For a much more detailed, parent-friendly guide to how children are taught about each of these concepts in English, as well as examples, click on the link in the word. Mark Warner The following page outlines a variety of activities relating to the theme "instructions" which can be carried out in the classroom. Before you try them, it might be a good idea to collect a set of instructional texts and resources, such as: Ask them to read the instructions and discuss what they are for. They should also evaluate the instructions in terms of ease of use Are the instructions clear? Would you be able to follow them to achieve the desired outcome? Is the chosen presentation appropriate? Would you prefer more diagrams or more text? The children would have to choose appropriate vocabulary for the level of the intended audience. Jumble up the sections, and ask the children to put them into the correct order. In the story, George makes four different medicines, so the class could make instructions for one, or for all four comparing them to see what why the last three did not have the same effect as the original. For example, if they were interested in animals, they could make some instructions showing how to care for animals properly. If they liked computers, they could explain how to play their favourite computer game. This activity might require some time beforehand for the children to find out more information about their topic. If the children have just designed and made a project, they could write some instructions telling others how to make their project, or how to use it properly. This will encourage them to use text and pictures in their instructions, and to break their instructions down into a number of small steps. I let them go around the building one team at a time. Then they give their directions to another team to follow exactly as they wrote them even though they know how to get to the places! They report back as to where they ended up. It really emphasises the need for specific directions. I like to do this as the opening activity so they are focussed on giving the best details they can when they write their own instructions.This list of grants has been compiled to aid schools, youth groups, the environmental, outdoor and play sectors with finding funding for a range of outdoor ventures and initiatives. ST. LUKE’S RC PRIMARY SCHOOL NEWSLETTER 2 nd NOVEMBER Dear parents. PARENTS’ EVENING. As you are aware we are holding our first Parents’ Evening of the year next Wednesday 7 th November.. May we respectfully remind you that these appointments are for parents only, children must not be brought into school as we cannot provide a crèche.. KEY RADIO MISSION CHRISTMAS. Instructions (KS2 resources) KS1 and KS2 ideas for instruction writing, including instruction writing frames, instruction examples, instructional texts and instruction comprehension activities and . Mar 10, · The Instruction Writing Pack contains a wide range of printable activities and resources to use in your Literacy lessons. A fantastic set of teaching materials and independent activities to support and enhance your children's instructional writing/5(26). This website can only be accessed by treatment schools taking part in ReflectED Trial If you are a treatment school and would like to access resources, please log . Funbrain is the leader in online educational interactive content, with hundreds of free games, books & videos for kids of all ages. Check out Funbrain here.

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Convolution is a mathematical operation that does the integral of the product of 2 functions(signals), with one of the signals flipped. For example below we convolve 2 signals f(t) and g(t). So the first thing to do is to flip horizontally (180 degrees) the signal g, then slide the flipped g over f, multiplying and accumulating all it's values. The order that you convolve the signals does not matter for the end result, so conv(a,b)==conv(b,a) On this case consider that the blue signal is our input signal and our kernel, the term kernel is used when you use convolutions to filter signals. Output signal size 1D In the case of 1D convolution the output size is calculated like this: Application of convolutions People use convolution on signal processing for the following use cases: - Filter signals (1D audio, 2D image processing) - Check how much a signal is correlated to another - Find patterns in signals Simple example in matlab and python(numpy) Below we convolve two signals x = (0,1,2,3,4) with w = (1,-1,2). Doing by hand To understand better the concept of convolution let's do the example above by hand. Basically we're going to convolve 2 signals (x,w). The first thing is to flip W horizontally (Or rotate to left 180 degrees) After that we need to slide the flipped W over the input X Observe that on steps 3,4,5 the flipped window is completely inside the input signal. Those results are called 'valid' convolutions. The cases where the flipped window is not fully inside the input window(X), we can consider to be zero, or calculate what is possible to be calculated, e.g. on step 1 we multiply 1 by zero, and the rest is simply ignored. In order to keep the convolution result size the same size as the input, and to avoid an effect called circular convolution, we pad the signal with zeros. Where you put the zeros depends on what you want to do, ie: on the 1D case you can concatenate them on each end, but on 2D it is normally placed all the way around the original signal. On matlab you can use the command 'padarray' to pad the input: >> x x(:,:,1) = 1 1 0 2 0 2 2 2 2 1 0 0 0 2 1 2 2 2 2 1 2 0 2 2 1 x(:,:,2) = 2 1 0 0 0 0 2 0 1 0 1 0 1 2 0 1 2 0 2 1 1 2 1 2 2 x(:,:,3) = 2 1 1 2 2 1 1 1 0 0 2 0 1 0 2 0 2 0 2 1 0 0 2 1 0 >> padarray(x,[1 1]) ans(:,:,1) = 0 0 0 0 0 0 0 0 1 1 0 2 0 0 0 2 2 2 2 1 0 0 0 0 0 2 1 0 0 2 2 2 2 1 0 0 2 0 2 2 1 0 0 0 0 0 0 0 0 ans(:,:,2) = 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 2 0 1 0 0 0 1 0 1 2 0 0 0 1 2 0 2 1 0 0 1 2 1 2 2 0 0 0 0 0 0 0 0 ans(:,:,3) = 0 0 0 0 0 0 0 0 2 1 1 2 2 0 0 1 1 1 0 0 0 0 2 0 1 0 2 0 0 0 2 0 2 1 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 Transforming convolution to computation graph In order to calculate partial derivatives of every nodes inputs and parameters, it's easier to transform the operation to a computational graph. Here I'm going to transform the previous 1D convolution, but this can be extended to 2D convolution as well. Here our graph will be created on the valid cases where the flipped kernel(weights) will be fully inserted on our input window. We're going to use this graph in the future to infer the gradients of the inputs (x) and weights (w) of the convolution layer. Now we extend to the second dimension. 2D convolutions are used as image filters, and when you would like to find a specific patch on an image. An example of filtering is below: Matlab and python examples Doing by hand First we should flip the kernel, then slide the kernel on the input signal. Before doing this operation by hand check out the animation showing how this sliding works. By default when we're doing convolution we move our window one pixel at a time (stride=1), but some times in convolutional neural networks we want to move more than one pixel. For example on pooling layers with kernels of size 2 we will use a stride of 2. Setting the stride and kernel size both to 2 will result in the output being exactly half the size of the input along both dimensions. Observe that below the red kernel window is moving much more than one pixel at a time. Output size for 2D It is useful to know what the dimensions of our output are going to be after we have performed some convolution operation to it. Luckily there is a handy formula that tells us exactly that. If we consider convolving an input, of spatial size [H, W] padded by P, with a square kernel of size F and using stride S, then the output size of convolution is defined as: F is the size of the kernel, normally we use square kernels, so F is both the width and height of the kernel Implementing convolution operation The example below will convolve a 5x5x3 (WxHx3) input, with a conv layer with the following parameters Stride=2, Pad=1, F=3 (3x3 kernel), and K=2 (two filters). Our input has 3 channels, so we need a 3x3x3 kernel weight. We have 2 filters (K=2) so we will have 2 output activations at the end. Also we can calculate the size of these two outputs to be: (5 - 3 + 2)/2 + 1 = 3. So we will get a final output volume of size (3x3x2). Looking at this example in more detail, basically we need to calculate 2 convolutions, one for each 3x3x3 filter (w0,w1), and remembering to add the bias. The code below (vanilla version) cannot be used in real life because it will be slow but its good for a basic understanding. Usually deep learning libraries do the convolution as one matrix multiplication, using the im2col/col2im method. %% Convolution n dimensions % The following code is just a extension of conv2d_vanila for n dimensions. % Parameters: % Input: H x W x depth % K: kernel F x F x depth % S: stride (How many pixels he window will slide on the input) % This implementation is like the 'valid' parameter on normal convolution function outConv = convn_vanilla(input, kernel, S) % Get the input size in terms of rows and cols. The weights should have % same depth as the input volume(image) [rowsIn, colsIn, ~] = size(input); % Get volume dimensio depthInput = ndims(input); % Get the kernel size, considering a square kernel always F = size(kernel,1); %% Initialize outputs sizeRowsOut = ((rowsIn-F)/S) + 1; sizeColsOut = ((colsIn-F)/S) + 1; outConvAcc = zeros(sizeRowsOut , sizeColsOut, depthInput); %% Do the convolution % Convolve each channel on the input with it's respective kernel channel, % at the end sum all the channel results. for depth=1:depthInput % Select input and kernel current channel inputCurrDepth = input(:,:,depth); kernelCurrDepth = kernel(:,:,depth); % Iterate on every row and col, (using stride) for r=1:S:(rowsIn-1) for c=1:S:(colsIn-1) % Avoid sampling out of the image. if (((c+F)-1) <= colsIn) && (((r+F)-1) <= rowsIn) % Select window on input volume (patch) sampleWindow = inputCurrDepth(r:(r+F)-1,c:(c+F)-1); % Do the dot product dotProd = sum(sampleWindow(:) .* kernelCurrDepth(:)); % Store result outConvAcc(ceil(r/S),ceil(c/S),depth) = dotProd; end end end end % Sum elements over the input volume dimension (sum all the channels) outConv = sum(outConvAcc,depthInput); end

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This unit includes: In this unit students will develop an understanding of equivalent fractions using common denominators. Lessons are designed so that students begin working with concrete materials, then move to pictorial drawings to represent their thinking, and finally solve for equivalent fractions using numbers only. Each lesson contains a MINDS ON TASK CARD, an EXIT CARD, and an EXTRA PRACTICE WORKSHEET. Lessons have MODELLED examples and opportunities for SHARED, GUIDED, and INDEPENDENT practice. How To Make Equivalent Fractions Using Fraction Strips How To Make Equivalent Fractions Using Counters (Arrays/Ratios) How To Make Equivalent Fractions Using Pictorial Drawings How To Make Equivalent Fractions Using Numbers Only How To Solve Problems Involving Equivalent Fractions

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The diagram shows a cone with a radius of 20 centimeters and a perpendicular height of 40 centimeters. We’re told that the volume of a cone is equal to a third times the area of its base times its perpendicular height. And we’ve got to work out the volume of the cone, giving our answer in terms of 𝜋. Now we can see that our cone has a circular base with a radius of 20 centimeters. And we can see that the perpendicular height is 40 centimeters. And the fact that our diagram had this little right angle symbol here helped us to identify the fact that it was in fact a perpendicular height. Now, it’s important to remember when you’re calculating the volume of a cone that you do take the perpendicular height of that cone and not the slant height, the length of the slopy side of the cone. Now, we should also notice that we’ve been asked to give our answer in terms of 𝜋. And this just means as a multiple of 𝜋. Now in this particular question, we can’t express the answer as an exact decimal. We’d need to round it to a few decimal places. And then, it wouldn’t be fully accurate. But by giving it as an exact number multiplied by 𝜋, we are representing the exact answer. So let’s start our working out by just copying out that formula that we were given earlier in the question. “Volume equals a third times the area of the base times the perpendicular height.” Now, all of the dimensions that we were given in the questions were in terms of centimeters. So our volume is going to be in cubic centimeters. And we know that the perpendicular height was 40 centimeters. So we need to work out the area of the base of our cone. Well, a cone has a circular base. And the formula for the area of a circle is 𝜋 times the radius squared. Now, it’s important to remember that it’s only the radius that’s squared. We don’t end up squaring 𝜋 as well. And we know that the radius is 20. So the formula for our volume becomes a third times 𝜋 times 20 squared times 40. And then, the units are gonna be cubic centimeters. Now, 20 squared means 20 times 20. And that’s 400. Now, we can think of 400 as being four times 10 times 10. And 40 is just four times 10. Now it doesn’t matter what order we multiply those numbers together in. We’re gonna get the same answer. So I’m gonna say four times four is 16. 16 times 10 is 160, times 10 again is 1600, times 10 again is 16000. So that gives us a third times 𝜋 times 16000 cubic centimeters. Again, it doesn’t matter what order we multiply these things together in. We’re still gonna get the same answer. So I’m gonna swap the 𝜋 and the 16000 around. And 16000 is the same as 16000 over one. It’s just a fraction form of the same number. So now, I’ve got a third times 16000 over one. This is a fraction calculation. I can multiply the one and the 16000 together and the three and the one together. So that’s 16000 over three times 𝜋, but more simply, 16000 over three 𝜋 cubic centimeters. So we’ve given our answer as a multiple of 𝜋. In other words, we’ve given our answer in terms of 𝜋. The fact that the number we’ve got is a top heavy fraction doesn’t really matter. It’s a perfectly acceptable way to present your answer. Now, if you’ve got your calculator with you, you may be tempted to turn that top heavy fraction into a mixed number like this, 5333 and a third 𝜋 cubic centimeters. And that’s absolutely fine. There’s absolutely no need to do it. But you can do it if you want to. If you do stop messing about with your calculator, it may give you an answer like this 5333.3 recurring 𝜋 cubic centimeters. And that’s not quite exact. 0.3 recurring isn’t quite the same as a third. So that’s not an exact answer. I wouldn’t advise doing that. And if you go the extra step and actually multiply by 𝜋, you’ll get an answer like this, 16755.16082 and so on cubic centimeters. That’s wrong because the question asked us to specifically give our answer in terms of 𝜋. So don’t be tempted to do more work than you need to. Just give your answer in the simple form I’ve asked for, as a multiple of 𝜋.

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- compare and contrast the characteristics of two different Medal of Honor Recipients - debate whether a person’s size or intellect makes a difference in his/her contribution to society - stand up for people who are not able to stand up for themselves - recognize what bullying is and is not |SUGGESTED LEVEL||SUGGESTED APPLICATIONS| |Middle and High School||Language Arts| One to Two Class Sessions Start a class discussion by asking the class a few questions: - Do they know other students who have been bullied based on size and/or other characteristics? - What would it be like for those students to be star athletes, or part of the “cool kids”? - What if the popular students were suddenly outcasts? Clarify bullying and what it looks like. Definition: Bullying is unwanted, aggressive behavior among school-aged children that involves a real or perceived power imbalance. The behavior is repeated, or has the potential to be repeated, over time. Bullying includes actions such as making threats, spreading rumors, attacking someone physically or verbally, and excluding someone from a group on purpose. There are many roles that kids can play. Kids can bully others, they can be bullied, or they may witness bullying. When kids are involved in bullying, they often play more than one role. It is important to understand the multiple roles kids play in order to effectively prevent and respond to bullying. Small Group/Individual Activity: Students will write a short reflection in response to these questions: - What do you think bullying is? - Have you been bullied, or do you know someone who has been bullied? - What were (are) the circumstances? - What could you have done or what can you do to help the person being bullied? Whole Group Activity: Use masking tape to place a line down the middle of the classroom. One side is for students who belong to clubs, sports, enjoy school, and have what they believe are lots of friends. The other side is for students who may not belong to any school clubs or activities, tend to cause mischief, or who think of themselves as outcasts or different. The teacher will use quotations from the two videos shown later during the whole group activity below. The quotations need to be from both Recipients. Students will choose a side based on the quotations with which they personally identify (Naughty, Not much into school, etc.). Students who are not sure may stand on the center line. For those having a hard time choosing, students will be asked to choose a side that best describes a friend (This is an opportunity to avoid embarrassment or to help speed up the decision-making process). Once the quotations and directions are read, students will step to the appropriate side of the room. The teacher may use the students on the line to even out the sides as needed. Give one side of the room the nickname “Jackson’s Brigade.” Let the other side know they are “Nick’s Battalion. Whole Group Activity: Students will view both videos. If necessary, use a graphic organizer and pause during the video to give students a chance to internalize what they are viewing. After watching these two different types of heroes with physical and intellectual differences, students will defend the hero they are representing. The challenge is to decide which story was more amazing and a greater accomplishment. Each side of the room elects two speakers to represent their groups. Groups can call a collaboration meeting as needed during the debate. The two teams will debate the accomplishments presented in their hero’s stories, taking into consideration size, situation, help, equipment, and outcome. Students will list on the board the common characteristics of both heroes. The entire class will brainstorm other professionals or individuals they see in society with these same characteristics. Individually students will write an essay explaining whether their view of military heroes has changed or whether the typical Hollywood stereotype is valid. Reflection assignment, essay

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Here are suggested activities linked to your weekly overview for Week 7 (25.05.20). This week's focus is Fractions. You should have a little bit of knowledge about fractions from P3/4 and your mental maths tables. Spend some time watching the videos and looking through the PPTs which will help you through this area of Numeracy. For the lessons, you’ll have a few worksheets you can complete linked to your Numeracy group. Please make sure you choose the correct activity. You do not need to do all the worksheets for all the groups...just your group. Remember to check out Studyladder too where you will find a Fractions POD to work on. If you need any help or further explanations... please email your teacher. We are only too happy to help. Numeracy Lesson 1 – Introduction to Fractions What is a fraction? A fraction represents part of a whole. When something is broken up into a number of parts, the fraction shows how many of those parts you have. Pictures of Fractions Sometimes the best way to learn about fractions is through a picture. See the pictures below to see how the whole of a circle can be broken up into different fractions. The first picture shows the whole and then the other pictures show fractions of that whole. Numerator and Denominator When writing a fraction there are two main parts: the numerator and the denominator. The numerator is how many parts you have. The denominator is how many parts the whole was divided into. Fractions are written with the numerator over the denominator and a line in between them. Have a look at the following videos and PPTs which explain a little more about talking about fractions of things. If you think you’ve got this…why don’t you try playing the following games to help you practice and then try your worksheets for today if you can. Numeracy Lesson 2 – Finding a Fraction of a Number Yesterday we spent some time looking at what fractions were and shading some fractions. Today we’d like you to find fractions of numbers. You were practising this a few weeks ago in your weekly tables. You need to remember: D for Denominator = D for dividing To find a fraction of a particular number, you divide by the bottom number. Have a little watch at the following video. It goes into finding ¾ etc. of a number, but in P5, we just need to focus on finding ½, ¼ etc. So it’s really easy: 1/5 of numbers means to divide by 5, so… 1/5 of 25 = 25 divided by 5 = 5 etc. 1/3 of number is dividing by 3, so… 1/3 of 24 = 24 divided by 3 = 8 Why don't you practice these tables here (Please only choose numbers with a 1 on the top (Numerator))? If you want to find more than 1/3 of something, e.g. 2/3 why don’t you have a read here which explains this a little further. You can have a try at this at the bottom of Worksheet 2 and you’ll need this skill to complete the Fraction Avenue Extension Activity too. A step further is to find the fraction of larger numbers by doing a written division sum. This may be important in real life when you need to find the fraction of the cost of something. Why don’t you practice your written division by having a go at some of these? Use your workbook and give them a go. Numeracy Lesson 3 – Equivalent Fractions Sometimes fractions may look different and have different numbers, but they are equivalent or have the same value. One of the simplest examples of equivalent fractions is the number 1. If the numerator and the denominator are the same, then the fraction has the same equivalent value as 1. When fractions have different numbers in them, but have the same value, they are called equivalent fractions. This means that they are EQUAL! Let's take a look at a simple example of equivalent fractions: the fractions ½ and 2/4. These fractions have the same value, but use different numbers. You can see from the picture below that they both have the same value. How can you find equivalent fractions? Equivalent fractions can be found by multiplying or dividing both the numerator and the denominator by the same number. Watch the following videos which explain Equivalent fractions a little more. (Please ignore the American video where they refer to quarters as ‘fourths’. We’d prefer you to use quarters) Maybe you have some Lego or blocks at home. These can help you lots with your fractions and especially with your equivalent fractions. Have a watch of this video to see how. Why don’t you have a go at the following worksheets taking your time and working carefully. You can do it! Use this link to an interactive fraction wall to help you with the worksheets https://www.visnos.com/demos/fraction-wall , or you could print off the fraction wall and colour it in or you could make your own fraction wall from Lego. If you think you’ve mastered equivalent fractions, have a go at playing this game. It’s a good one and makes you think about your fractions. Don’t forget to use your fraction wall to help you if you wish. Lesson 4 – Making 1 whole thing or subtracting from 1 whole We would also like you to think about making 1 whole thing and taking fractions away from 1 whole thing. It may be useful to use a fraction wall to help you do this. There is a picture of one below and a link to an interactive one. So, if I had 6/11 and I wanted to make 1 whole thing. How many more ‘elevenths’ would I need? Well, how many ‘elevenths’ make one whole thing…that would be 11. If I already have 6 of them, then I need another 5 and the answer would be 5/11 (5 elevenths). If I was trying to subtract from 1 then you need to think about your bottom number again – it’s called the denominator which basically means, it’s the boss! 1 – 5/7 =? If I started with 1 whole thing and wanted to take away 5/7 (5 sevenths). Well how many sevenths would make a whole thing? That would be 7. If I take 5 of them away, then I am left with 2 and my answer is 2/7 (2 sevenths). Why don’t you practice by playing the following game and then trying your worksheets for today? Always try to visualize you fractions in pizzas…..YUM!

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Do your students need extra practice with irregular past tense verbs? This simple sheet will clue them in! Students will convert present tense verbs to past tense verbs using the number of letter blanks to help guide them to the proper spelling. It's time to find out if your second graders have successfully mastered those tricky irregular past tense verbs. Assess your students’ understanding of common irregular past tense verbs with this end-of-year activity. Assess student understanding of common spelling patterns for vowel sounds with this quick sorting exercise. Young readers will read words and then write them out in the appropriate column for long or short vowel sounds. Have your second graders conquered those tricky irregular plural nouns? Time to find out! Assess your students abilities to change irregular nouns from singular to plural with this quick assessment activity. Word puzzles are an effective and entertaining way to practice irregular past tense verbs with your students. Let your budding wordsmiths have fun reviewing those tricky past tense verbs with this crossword puzzle! Compound words are just words that are made by putting two smaller words together. With this worksheet, students will work backwards from definitions to guess the compound words and expand their vocabulary. Give kids a fun way to practice using parts of speech with this fill-in-the-blank story template! You and your students will be in a fit of giggles as you listen to each other read their completed zoo-inspired stories aloud! The grammar game gets ramped up in second grade, with the introduction of such concepts as plurals, adjectives, adverbs, subject and object pronouns, and present and past tense. Our second grade grammar worksheets cover all of this material, and a whole lot more. And with dozens of crossword puzzles, word searches, matching games, and sentence scrambles, our second grade grammar worksheets entertain young students while improving their writing, reading, and speaking abilities.

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Students will be able to - recognize that if a current-carrying wire is placed in a magnetic field, there will be a force on it and it may move, - recognize that the wire must be placed perpendicular to the magnetic field for the magnitude of the force to be greatest, - recognize that if the wire is placed parallel to the field, there will be no force on it, - work out the direction of the force using Fleming’s left-hand rule, - use in all permutations. Students should already be familiar with - what electric current is, - the idea that permanent magnets can attract or repel each other, - what a force is. Students will not cover - cases in which the angle between the wire and the field is neither nor , - what happens in nonuniform magnetic fields/time-varying magnetic fields, - what happens when the wire is curved/anything other than straight, - what happens when the wire has an alternating current, - the effect of magnetic fields on charged particles/beams of charged particles, - torque on loops of wire.

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This Kindergarten: Number and Operations in Base 10 K.NBT.1 lesson plan also includes: - Join to access all included materials Do your mathematicians enjoy using counting cubes? First, have them create a tens stick in pairs. Then hand out nine individual cubes per partnership, as well as number cards 11-19. As they choose a number card, learners help each other represent the number using the cubes. A worksheet helps them organize their work through writing number sentences, which are mapped out for them. This activity will require modelling. - This resource is only available on an unencrypted HTTP website. It should be fine for general use, but don’t use it to share any personally identifiable information

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First grade mathematicians will be working this year on number sense in order to improve their understanding of the relationship between numbers and their ability to do mental math. This guided lesson will help strengthen this important skill with targeted instruction and plenty of real-world practice problems. Once the lesson is finished, you can extend learning with the suggested number sense worksheets. In this introduction to numbers 0-20, kids practice what they've already learned about the numbers 0-10 and build new skills in counting 11-20. Not only will preschoolers practice recognizing these numerals, but they will also be given rote count to 20 exercises to reinforce skills. Approaching numbers in a scaffolded way such as this helps build math fluency and boosts confidence. Knowing how to build numbers is an important lesson for kindergarteners just getting their feet wet with counting and numbers. These guided exercises can give kids a deeper understanding of number sense, numerical order, and values. Kindergarteners will begin to associate values with numbers and comprehend the concepts of greater than and less than, building upon skills they will need in the later grades. In this lesson, kindergarteners will be given the chance to focus on their counting skills with engaging exercises and guided instruction. Just as identifying the letters of the alphabet is a precurser to reading, so is counting to developing math fluency. Soon, your child will learn that the numbers they are counting have associated values, so the more practice they can get with counting the better. Once your students have grown comfortable with the numbers 0-10, they have a solid foundation for learning double-digit numbers. Students playing speed counting games and completing number maze worksheets will be able to quickly identify the numbers 11-20. From there, Education.com workbooks will teach students how to easily determine which of the numbers in a pair is greater or lesser.

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When parts of the mantle or crust melt, magma is formed. Within these magma chambers, gases in the chambers are causing an increase in pressure. As the pressure gets higher, the magma moves up. It moves up into the “throat” or the volcano, and thus causing an eruption. During some eruptions, you can even see lightning due to ash particles that cause electric sparks. A volcano is a surface landform resulting from the extrusion of magma from underground as lava, ash, rocks, and gasses are erupted in various proportions. A hazard is something that poses a threat to life, the environment or property. Volcanoes can compromise all these things through the many hazards volcanoes presents. These include lahars, flash flooding, landslides, pyroclastic flows, ash clouds and many others. Each year, around 60 major volcanoes erupt globally. Thicker, more viscous magma has a greater potential for explosive eruptions and therefore represent the greatest potential hazards. The thickest type of magma is known as Acid Magma. Its relatively low temperature (600C-1000C), high silica content and low proportion of dissolved gases causes its toothpaste-like consistency that leads to blockages and powerful eruptions. This can mean that the eruptions caused by thick magma can be less frequent and more difficult to predict, meaning that when an eruption does occur, it is usually with little or no warning, which can lead to catastrophic consequences as any nearby settlement will be relatively unprepared for the effects of a violent volcanic eruption. Furthermore, acid magma is more likely to produce clouds of smoke and ash due to the explosive nature of the eruption it causes, than thinner, basic lava. The difference in pace and movement of plates, triggers the up build friction. When this friction is released- Earthquakes are generated. An example of an event is the San Francisco earthquake in 1989 on October 17 measuring 6.9 on the Richter scale. Tsunamis are one result of earthquakes. A sudden shift in It allows us to understand how sedimentary rocks, metamorphic rocks, and Igneous Rocks use one another to not only form the Rock Cycle, but also other processes that are important to our planet. The rock cycle beings with hot magma, deep below the earth’s surface. Once the magma dries, crystallization occurs, and results in igneous rocks. Over time weathering occurs to the igneous rocks. Over time weathering takes over the igneous rocks. Volcanoes are found mainly in three locations, at constructive and destructive plate margins and at hotspots. The most dangerous volcanoes occur at destructive, convergent plate margins. Here one plate subducts beneath the other, and as it descends, friction, increasing pressure, and heat from the asthenosphere and mantle melt the plate to form an acidic magma chamber. The magma at these boundaries is andesitic and rhyolitic, meaning that they have a high viscosity. Because of this the lava is resistant to flow and often forms blockages in vents. In which ways does volcanic activity vary in relation to the type of plate margin along which it occurs? (10 Marks) Volcanic activity can occur at constructive or destructive plate margins, but it can also occur at hotspots in which no plate margin is involved. At destructive margins two plates which are moving together can be either both oceanic plates or one continental and the other oceanic. In the case of one continental plate and one oceanic plate, volcanic eruptions are very violent and emit andesitic or rhyolitic lava. These types of lava are very viscous due to its high silica content. This knowledge of plate margins and their movement against one another can help us to understand the distribution of seismic and volcanic events and this is because the majority of events are associated at these plate margins. Wegener’s theory of plate tectonics suggests that all the continents were once joined together in a super continent called Pangea and have since drifted apart due to plate tectonics. To add to this, Sea floor spreading was discovered showing that rock is being created and destroyed, leading us to believe in the existence of plates and plate boundaries. Wegener gained evidence from paleo magnetism and suggested that there were numerous reasons and pieces of evidence for the continents drifting apart. Biologically, there was evidence that proved his theory for example, the Mesosaurus reptile fossils were only found in Africa and South America, proving his ‘jig-saw’ fit idea. The nature of an event is initially determined by how the cause was stimulated. Volcanic eruptions occur in many different forms determined by the plate margin they are on. The eruptions on Montserrat 1995 show a strong example of the nature of a volcano at a destructive plate margin. The Soufriere Hills volcano had lay dormant for a long period of time. When the eruption did occur it was seen as explosive as it produced large volumes of acidic lava, ash, pyroclastic flows and steam. Gases dissolved in magma provide the motive force of volcanic eruptions, sulphurous volcanic gas and visible steam are usually the first things noticed on an active volcano as well as others that escape unseen for example through hot fumaroles, active vents, and porous ground surfaces. The limitations of taking these samples are remote location of these sites, intense and often hazardous fumes, frequent bad weather, and the potential for sudden eruptions can make regular sampling sometimes impossible and dangerous. Measuring gases remotely is possible but requires ideal weather and the availability of suitable aircraft or a network of roads around a

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We live in an increasingly diverse society, one in which being an American can mean many things. This diversity is especially apparent in our public schools. In fact, the National Center for Education Statistics predicts that children of color will make up 56% of students in public schools by the fall of 2029. As a result of this demographic shift, educators across the country have begun to develop more inclusive curricula that address their students’ cultural backgrounds. By swapping the outdated “colorblind” approach for a “color aware” model, teachers encourage students to share their experiences and become more accepting of one another’s perspectives. If you want help incorporating a multicultural educational program into your school’s classrooms, please consider Positive Action, a complete multicultural curriculum for students in preschools, elementary schools, and secondary schools. You can jump directly to a different section from this page by using the list below: Our socially-focused multicultural curriculum aims to reduce bias by teaching students that we feel good about ourselves when we do positive actions, which include treating others how we want to be treated—regardless of cultural backgrounds. By emphasizing values like empathy and respect, the Positive Action model effectively teaches students to understand people from a variety of cultures. Through stories and role-playing exercises, students learn that living among people with different backgrounds makes our world a better place. Teaching students to treat each other kindly leads them to see life from other people’s perspectives, gaining a better understanding of those from different cultural groups. Our multicultural curriculum for the youngest students begins with two hedgehog puppets, Squeak and Mimi, who meet new friends from totally different cultures. Throughout a story complete with helpful visual materials, the characters recognize that they must get along to live in harmony. From kindergarten through fifth grade, the Positive Action educational content features human characters in relatable social situations, like learning how to make friends in a foreign community. Students learn that they can create meaningful friendships anywhere. As a result, they develop positive feelings about people from many different cultures. Using teaching materials that describe fictional scenarios, students address issues that they face in their classrooms and discuss them using critical thinking skills. The eighth-grade curriculum concludes with a challenge to “broaden your horizons” as a way to encourage students to explore diverse perspectives and understand people from different groups. The content for our oldest group of students consists of four kits that you can complete in any order. Rather than storybook teaching materials, these curricula incorporate a variety of formats for different learning styles, including creative projects, community service, and peer leadership. In the latter, all of the students have the chance to be leaders as they teach each other about ideas like the Golden Rule—a concept with a deep history in more than 270 cultures. Each Positive Action kit includes the materials for two free, downloadable sample lessons from our multicultural education curriculum. As an evidence-based curriculum, the Positive Action multicultural education program results in tangible improvements that teachers can see among their students, including: Learn the ways that students, teachers, and communities across the nation have used Positive Action’s multicultural education program to create environments more accepting of diversity: “What is helpful is that the Positive Action program is compatible with our Native American values and ethics. We want to celebrate who we are and improve on that.” –Marlene Harrell, principal and federal programs administrator at the Frazer School District (Frazer, MT) “Positive Action teaches empathy and acceptance of others. It provides a foundation for the children to fall back on when there is a situation that happens on the playground or when there is a new student.” –Suzee Fujihara, teacher at Lihikai Elementary (Lihikai, HI) Compared to other multicultural education programs, Positive Action provides the most content, meets the most state and national standards, and offers the most support, training, teaching, and learning resources. Multicultural education focuses on students’ development of a broader understanding of our diverse world. Students learn to value one another’s cultural history and appreciate diverse perspectives. The teachers play a major role in this educational model. They listen to students’ experiences and address both social and institutional inequalities between different cultural groups, helping everyone understand the challenges their peers face and the accomplishments they’ve achieved. This diversity-centric curriculum helps students feel understood and empowered to succeed within the classroom and beyond. Experts refer to multicultural education as a process because educators should constantly work toward reaching these goals. In particular, multicultural education covers five important areas: Content integration: Teachers must include the history, concepts, and values of a variety of cultures in their educational content. Knowledge construction: Educators must reevaluate their perspectives and construct new, bias-free alternatives. Equity pedagogy: In education, equity means providing students in different groups with the resources they need to achieve an equal outcome. Bias reduction: Teachers must help students become more accepting of people different from them. School culture empowerment: The school’s guiding beliefs and values must include cultural acceptance. By eliminating bias within the walls of the classroom, educators will help students emerge better prepared to interact with diverse groups in a variety of social and professional settings. Learning about and accepting other cultures will serve them well whether they plan to attend a university or enter the workforce immediately after graduation. On the flipside, multicultural inclusion is critical to making members of minority groups feel welcome and safe in an American education setting, as well as in society at large. Society itself will benefit, too. Learning about others’ cultural experiences in the classroom will inhibit the development and spread of prejudice going forward—a must for societal growth. Whether they teach preschool or university students, educators can do many things to create a multicultural education experience, including the following: Recognize biases: Knowing what bias looks like—be it racial, religious, or otherwise—means being able to spot it in your students as well as in yourself. Teachers must work toward rooting out these harmful perspectives. Value students’ life experiences: Encouraging students to share their experiences is critical to exposing their peers to other perspectives as well as providing the sharers with powerful validation. Understand students’ learning styles: Students process information in a variety of ways, including visual, auditory, and tactile methods. Education should incorporate all styles to reach all students. Include other cultures in your teaching materials: Educators must teach their students about the history and vibrancy of other cultures. Teaching students about other backgrounds may involve assigning cultural content to read, presentations about family traditions, and other projects. If you want to see how Positive Action can encourage your students to learn about and embrace others’ perspectives, please let us know when you’re available for a webinar, and we’ll help you introduce our multicultural education program to your classroom. Of course, you can always contact us via phone, chat, or email as well.

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Q1. Identify the impact of the Fugitive Slave Act on the African American population and the ways in which individuals and organizations in black communities responded? The Fugitive Slave Act of 1850 made it easier for runaway slaves to be captured and returned to their masters. Northerners opposed the law; many northern states had passed personal liberty laws that forbade the kidnapping and forced return of fugitives. Personal liberty laws were ruled unconstitutional in Prigg v. Pennsylvania (1842); however, the Supreme Court did affirm that the return of fugitives was a federal matter, in which state officials could not be required to assist. 8. The new Fugitive Slave Act required federal marshals to pursue alleged fugitive slaves, and federal commissioners were appointed to oversee runaway cases. These officials received $10 for a runaway returned to the claimant and $5 for a runaway set free—which reflected the law’s bias. Northerners were most angered by the fact that federal marshals were authorized to call on citizen bystanders to aid in the capture of fugitives; bystanders who refused to help could be fined $1,000 and sent to jail for six months. Even northerners who had not given much thought to slavery were angered by what appeared to be the federal government exceeding its power. The new law frightened African Americans; even those who had escaped slavery years before could be returned to bondage. Fugitives fled from the United States and went to Canada, Mexico, and Europe for safety. 9. The new law also put free blacks at risk; an unknowable number of free blacks as well as fugitive slaves suffered enslavement or reenslavement at the hands of outlaw slave hunters. During the 1850s, 296 of 330 fugitives formally arrested, or 90 percent, suffered reenslavement. 1. After the Fugitive Slave Act of 1850 was passed, vigilance committees, which had at one time been all black, became increasingly interracial. These committees expanded the network of cellars, church basements, and other safe places where refugees could hide. 2. William Still and Harriet Tubman were important leaders of the underground railroad and vigilance committee antislavery network. Tubman, a runaway, personally traveled to the South at least fourteen times to help 130 slaves escape. Still published his stories about the network in The Underground Rail Road (1872). 3. In September 1851, near Christiana, Pennsylvania, a U.S. marshal and a party of slaveholders demanded to search the home of Eliza and William Parker—two runaways—for fugitives. Eliza sounded a large horn that summoned more than seventy-five local supporters to their home, where they killed a slaveholder and wounded his son. The Parkers and the other fugitives they were harboring escaped to Canada, but three white Quakers and thirty-five blacks were arrested for treason under the Fugitive Slave Act. Congressman Thaddeus Stevens assisted in their defense, and eventually the charges were dropped. 4. Harriet Beecher Stowe’s novel Uncle Tom’s Cabin (1852) graphically portrayed slavery’s devastating effects on families, encouraging empathy with slavery’s victims to increase support for abolition. At Solution Essays, we are determined to deliver high-quality papers to our clients at a fair price. To ensure this happens effectively, we have developed 5 beneficial guarantees. This guarantees will ensure you enjoy using our website which is secure and easy to use. Most companies do not offer a money-back guarantee but with Solution Essays, it’s either a quality paper or your money back. Our customers are assured of high-quality papers and thus there are very rare cases of refund requests due to quality concern.Read more All our papers are written from scratch and according to your specific paper instructions. This minimizes any chance of plagiarism. The papers are also passed through a plagiarism-detecting software thus ruling out any chance of plagiarism.Read more We offer free revisions in all orders delivered as long as there is no alteration in the initial order instruction. We will revise your paper until you are fully satisfied with the order delivered to you.Read more All data on our website is stored as per international data protection rules. This ensures that any personal data you share with us is stored safely. We never share your personal data with third parties without your consent.Read more

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Skip to main content It looks like you're using Internet Explorer 11 or older. This website works best with modern browsers such as the latest versions of Chrome, Firefox, Safari, and Edge. If you continue with this browser, you may see unexpected results. See Chapters 7 & 9 of the book. Use the periodic table to determine the number of valance electrons an element has. Use to the octet rule to determine how many electrons an element will gain or lose when it becomes an ion. Use the periodic table and the octet rule to determine the oxidation number of an element. Use the periodic table to determine the most common oxidation number for transition metals. Differentiate between a cation and an anion and what causes each. Determine whether or not a compound is ionic, given the formula or the name. Count the number of atoms in a chemical formula. Predict the chemical formula of an ionic compound (drop and swap method) for compounds with elements and/or polyatomic ions. Name ionic compounds, including using the stock system for transition metals, if given its formula. Write the chemical formula for an ionic compound if given its name.

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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. What Is a Random Variable? If you have ever taken an algebra class, you probably learned about different variables like x, y and maybe even z. Some examples of variables include x = number of heads or y = number of cell phones or z = running time of movies. Thus, in basic math, a variable is an alphabetical character that represents an unknown number.Well, in probability, we also have variables, but we refer to them as random variables. A random variable is a variable that is subject to randomness, which means it can take on different values. As in basic math, variables represent something, and we can denote them with an x or a y or any other letter for that matter. But in statistics, it is normal to use an X to denote a random variable. The random variable takes on different values depending on the situation. Each value of the random variable has a probability or percentage associated with it. Discrete Random Variables Let’s see an example. We’ll start with tossing coins. I want to know how many heads I might get if I toss two coins. Since I only toss two coins, the number of heads I could get is zero, one, or two heads. So, I define X (my random variable) to be the number of heads that I could get.In this case, each specific value of the random variable – X = 0, X = 1 and X = 2 – has a probability associated with it. When the variable represents isolated points on the number line, such as the one below with 0, 1 or 2, we call it a discrete random variable. A discrete random variable is a variable that represents numbers found by counting. For example: number of marbles in a jar, number of students present or number of heads when tossing two coins. X is discrete because the numbers that X represents are isolated points on the number line.The number of heads that can come up when tossing two coins is a discrete random variable because heads can only come up a certain number of times: 0, 1 or 2. Also, we want to know the probability associated with each value of the random. |# of Heads||Probability| In the table, you will notice the probabilities. We will see how to calculate the probabilities associated with each value of the variable. However, what we see above is called a probability distribution for the number of heads (our random variable) when you toss two coins. A probability distribution has all the possible values of the random variable and the associated probabilities. Continuous Random Variables Let’s see another example.Suppose I am interested in looking at statistics test scores from a certain college from a sample of 100 students. Well, the random variable would be the test scores, which could range from 0% (didn’t study at all) to 100% (excellent student). However, since test scores vary quite a bit and they may even have decimal places in their scores, I can’t possibly denote all the test scores using discrete numbers. So in this case, I use intervals of scores to denote the various values of my random variable.When we have to use intervals for our random variable or all values in an interval are possible, we call it a continuous random variable. Thus, continuous random variables are random variables that are found from measuring – like the height of a group of people or distance traveled while grocery shopping or student test scores. In this case, X is continuous because X represents an infinite number of values on the number line. Let’s look at a hypothetical table of the random variable X and the number of people who scored in those different intervals: |Test Scores||Frequency(% of students)| |0 to ;20%||5| |20% to ;40%||20| |40% to ;60%||30| |60% to ;80%||35| |80% to 100%||10| Since I know there are one hundred students in all, I could also have a column with relative frequency or percentage of students that scored in the different intervals. We calculate this by dividing each frequency by the total (in this case, 100). We then either leave the answer as a decimal or convert it to a percentage. Thus, like the coin example, the random variable (in this case, the intervals) would have certain probabilities or percentages associated with it. And this would be a probability distribution for the test scores. |Test Scores||Relative Frequency| |0 to ;20%||5%| |20% to ;40%||20%| |40% to ;60%||30%| |60% to ;80%||35%| |80% to 100%||10%| Probabilities Range Between 0 and 1 In the study of probability, we are interested in finding the probabilities associated with each value of these random variables. You may notice that, as a decimal, no probability is ever greater than one, nor are they negative. This is always true. For any designation of the random variable, the probability is always between zero and one, never negative and never greater than one. In math books, you will see this written as: Which says that P(X) is always between 0 and 1.The notation of P and then parentheses around X – P(X) – means the probability of X. Remember, X is the random variable. One note here: it does not matter if you use capital or common letters for the random variable or for P, as long as you are consistent! Sum of Probabilities for a Distribution Perhaps you noticed above that in each table the sum of all probabilities added up to 1 or 100%. However, for continuous random variables, we can construct a histogram of the table with relative frequencies, and the area under the histogram is also equal to 1. This graph is often called a density curve for the continuous random variable. Thus, a density curve is a plot of the relative frequencies of a continuous random variable. In math books, the property that the sum of the probabilities is given in short hand notation as: |The Greek symbol is called Sigma, capital sigma, and means sum. And so the statement says that the sum of the probabilities in a probability distribution equal 1. Some More Examples Let’s just look at a few examples of classifying random variables.Suppose I’m looking at the number of defective tires on the car. Let X = the number of defective tires on the car. Is X discrete or continuous? Well, since there are usually four tires on the car, X can range from 0-4. However, it can only be 0, 1, 2, 3 or 4. So X is a discrete random variable.Okay let’s look at another example. Suppose I am measuring the running time of movies that are currently playing in theaters in my city. Let X = the running time of movies. Is X discrete or continuous?Since movie times vary quite a lot and the length of the movie can be measured to the nearest minute or fraction of a minute or even seconds, depending on how accurate you want to be, X is a continuous random variable. When collecting my data, it would make sense to compile the data into intervals of running times as opposed to creating a category for each individual running time.One more example: You play a game where you toss a coin and record the number of tosses it takes to get two heads in a row. So let the random variable X = the number of times the coin is tossed to get two heads in a row. Using H for heads and T for tails, we could have sequences like these:HH two tossesTHH three tossesTTHH four tossesHTHH four tossesTHTHH five tossesTTTHH five tossesand so on …Is X discrete or continuous?Well for the above sequences X = 2, X = 3, X = 4, X = 5 and so on. ….But we can’t have 1. 5 tosses or 1.25 tosses. Thus, X is a discrete random variable.However, note that X can go on infinitely, since theoretically, we could toss forever and never get two heads in a row – although the probability of this happening is extremely small. But nonetheless, X is discrete since it represents isolated points on the number line (albeit these points go on forever). So let’s recap:A random variable is really just a variable that has certain values associated with it. In addition, each value of the random variable or each range of values of the random variable has probabilities associated with it.If the random variable represents isolated numbers on the number line, we call it discrete.If the random variable represents an infinite range of numbers or measurements, we call it continuous.Generally, discrete random variables are most often integers, and continuous random variables have a few to a lot of decimal places.We also saw that probabilities are always between zero and one, and the sum of the probabilities in a probability distribution equals one for a discrete random variable or the area under the density curve is one for a continuous random variable.So why the fuss over random variables? Well, by defining X, the random variable, to be something, it eliminates us having to write long sentences about what we are talking about, and we can now go on to calculating probabilities and generating probability distributions for our random variable X. Following this video lesson, you should be able to:

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The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo: As explained earlier, a force can be in the form of a push or a pull. A push force is applied when you try to move an object away from yourself. For example, when you apply an external force to move a table forward, you are using a push force. Similarly, when you move a table towards yourself, you are using a pull force. Hence a pull force is applied when an object is moved towards you. Let’s discuss some effects of the Force. Effects Of force On mass Let’s imagine we have two balls. One is heavier than the other. Now imagine you threw both balls with the same force. Which ball moves farther? To understand this, we need to understand that these balls’ mass affects them’ distance. A force cannot change an object’s mass but can alter the object’s speed and direction. Therefore, the heavier ball will travel less distance in comparison to the other ball. Hence the effects of force on mass are not changes in the weight of an object but changes in the object’s motion. Effects of force on speed As mentioned earlier, a force can change the speed of an object. When you apply force on a stable (resting) ball, it moves. The more force you apply, the faster it moves. When you apply additional force on a moving ball, it moves even faster. Following are the effects of force on speed of an object. Effects of force on the direction Suppose you apply force opposite to the direction of the moving object. What do you think would happen? The speed of the object reduces, and the object eventually stops. Given below are a few effects of force on the direction of an object: Force is of two types, As the name suggests, contact force is a force that is applied directly to the body, for example, mechanical force or muscular force. We use muscular force to lift an object. At the same time, the force generated by machines such as vehicles to move is called mechanical force. A unique example of contact force is friction. Not-Contact forces are the forces that act on the object without making any direct contact. These forces are not generated by touching the object but rather by external influence. For example, gravitational force, magnetic force, or electric forces are not created by direct contact. Friction is a type of force that resists the movement of an object. For example, if you move a table using force, why does it stop eventually? It stops because the force of friction is acting opposite to the force with which you pushed the table. Friction definition is the force that acts against the force of a moving object. It is a type of contact force, friction meaning the force produced when the surfaces of the object come in contact and act in the direction opposite to their motion. Without friction, an object keeps on moving on the surface. Therefore smooth surfaces have less friction, and rough surfaces have more friction (resistance). Key features of friction are The force of friction is of three types:

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Function notation is a fancy way of saying substitution. For example, if f(x) "f of x" = 2x + 5, then f(3) = 11 because 2(3) + 5 = 11. This shorthand is used to distinguish different Y values like R(x) = Revenue, C(x) = Cost and P(x) = Profit) in Finance where x is the number of units. In Physics, d(t) = Distance, v(t) = Velocity and a(t) = Acceleration where t is time. Understanding function notation is essential (and easy)! It has been added as a high school Math topic most likely because a calculator does not help if you do not know the notation. Tagged under: Function Notation,substitution Clip makes it super easy to turn any public video into a formative assessment activity in your classroom. Add multiple choice quizzes, questions and browse hundreds of approved, video lesson ideas for Clip Make YouTube one of your teaching aids - Works perfectly with lesson micro-teaching plans 1. Students enter a simple code 2. You play the video 3. The students comment 4. You review and reflect * Whiteboard required for teacher-paced activities With four apps, each designed around existing classroom activities, Spiral gives you the power to do formative assessment with anything you teach. Carry out a quickfire formative assessment to see what the whole class is thinking Create interactive presentations to spark creativity in class Student teams can create and share collaborative presentations from linked devices Turn any public video into a live chat with questions and quizzes

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Add using the make tens strategy. We can start with Unifix cubes, if necessary. For example, lay out Unifix cubes of length 2, 6, and 4. The student should recognize that 6 + 4 = 10, and from their work with teen numbers in Kindergarten, recognize that 10 + 2 = 12. Then we remove the Unifix cubes and ask the same question. Students are expected to say something like, 6 and 4 is 10, and I know 10 and 2 is 12, so the answer is 12. Conclude by leading this investigation: Speed Counting to Infinity 1.OA.B.3: Apply properties of operations as strategies to add and subtract. Students need not use formal terms for these properties. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

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Week 8: Math (9/20 - 9/24) Over the next two weeks, our math class will finish the chapter 1 lessons of learning how to connect, Put Together, and subtract, Take Apart, problems. Students are addressing real-life problems and learning the difference between practicing addition and subtraction. We will then take our post-test. The vocabulary words associated with this chapter are: Ways to Support Your Child at Home: There are many situations at home that you can use to model addition and subtraction. The kitchen is a great place to start! The maximum sum of objects for any activity in this chapter is 9. This aligns well with many cooking recipes. When preparing part of a meal, or baking goods, use the following strategies: • To model addition, separate the tomatoes, carrots, eggs, cups, or other food objects you are using for a recipe into two groups. Ask your student to count the number of objects in each group. Then ask, “How many are in each group? How many are there in all when I join the groups together?” • Show your student the number of objects you currently have to make a food item. Then tell your student that you need a certain number of these objects (9 or fewer) for the recipe. Ask, “How many more do I need?” • To model subtraction, show your student the number of objects (9 or fewer) you currently have. Then tell your student that you need a specific number of objects (fewer than the given group) for the recipe. Ask, “How many fewer do I need?” • Model other scenarios, making sure to use terms such as “take away,” “join,” and “difference.” By the end of this chapter, your student should feel confident with the learning targets and success criteria on the next page. Encourage your student to think of other opportunities related to cooking to use addition and subtraction contexts, such as buying items at a grocery store. Have a great time in the kitchen!

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Swan Class - Dividing Decimals by Integers Today, we will focus on the inverse of the lesson that we did yesterday. We will be looking at how we divide decimals. We will be looking at how this works in a practical, pictorial and abstract way first, before moving on to using the well-known bus stop method to divide decimals by integers. Many of you will remember how to use this method, so you should have little problem using it to divide decimals rather than whole numbers. Work through the tasks in the video and then use the sheets to give you a chance to apply what you have learned. Choose your challenge level. Don't forget to write in depth explanations, or give examples for reasoning problems that expect longer answers. They want to know how you know. Prove it to them. Fox and Magpie Class Algebra - Find a Rule Good morning. Today we kick off our learning about Algebra. There is a video below which explains the learning of today and a second one which explains the tasks for today. The tasks and answers are saved below. To start with, we are looking at the idea of a function machine (a calculation) which is acted upon an input (number) and then gives an output (an answer). For example if the input = 5 and the function = +10 then the output would = 15.

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Watch this video and more on Tech Learning Network Every program makes decisions. The coding structures used to make decisions are called conditionals. In this video, you'll learn to create simple conditional statements. Not every conditional is evaluated as true. In this section of the course, you'll create else statements to work with false conditions. The ternary operator is an abbreviated way of expressing a conditional-- Using it makes you look like a sophisticated Python programmer. You'll learn the ternary operator in this segment Almost everything in coding happens within the context of a loop. A loop allows you to repeat a section of code while some condition is true.

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Kindergartners have been working on number identification and counting to 5. First graders have been counting numbers from 0 - 10; 11 - 19; 20 - 29, 30 - 39, and now 40 - 49. First graders have also been learning about even and odd. Second graders have been skip counting by 2s, 5s, 10s, and 100s. They have also learned how to express a number in more than one way. Second graders can express a number in standard form, word form, expanded form, and in Base Ten blocks. Third graders have been learning how to use a number line to add and subtract. They have also been working on problem solving skills and knowing when to use addition or subtraction in word problems. Fourth graders have been working on rounding numbers to the nearest 10s, 100s, 1000s, and 10,000s. Fifth graders have been learning how to write expressions and compute numbers using order of operations. Fifth graders have also learned about factors and multiples, and prime and composite numbers.

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Highlighting a Word in the Text In scholarly writing, use italics or underlining. Italics and underlining are typically the favored methods of emphasis in academic or professional writing. These methods are easy to apply in a printed document; on the other hand, they are difficult to apply in an electronic document because there is no direct equivalent for either italics or underlining when editing word processing files. There are two ways to add italics to a word: Use the Ctrl+I keyboard shortcut or select the word and click the Italic button on the Formatting toolbar. Adding bold formatting to a word is similar; use the Ctrl+B keyboard shortcut or select the word and click the Bold button on the Formatting toolbar. Underlining works differently from both italics and bolding. To underline a word, select it and click the Insert Hyperlink button. The underlined word appears blue and can be clicked to open a new page where it will take you. Unlike italics or bolding, which only affect how the word appears in the document itself, an underline links the word to another place in the file. Even yet, italics or underlining are the recommended techniques to highlight words or phrases, particularly in academic writing. Writers often select one of two methods and utilize it consistently throughout an essay. Italics are typically utilized in the final, published edition of a book or article. Underlining is usually used in student essays and other scholarly works not intended for publication. The word "emphasize" can be used in a variety of ways in English. It can mean "to give importance to," "to put stress on (a particular word or phrase) in order to make it stand out from the rest of the text," or "to mark off (words or phrases) in bold type." Thus, emphasizing a word can be done by using italics, boldface, larger print, additional spaces between lines, or any combination of these techniques. In academic writing, emphasis is placed on specific words or phrases that require special attention. These highlighted words or phrases are called "academic terms" or "academic phrases." An example would be if you were writing about Leonardo da Vinci and wanted to focus on his creativity rather than his anatomy lesson, you might want to use italics or some other method of emphasis to draw attention to this word or phrase. There are three main methods of emphasis: typographical, linguistic, and substantive. Here are five typical methods for emphasizing text: However, italics and other font alterations lose their impact when used excessively. To get your argument clear, utilize such methods sparingly and rely on good writing and intelligent word placement. Prior to the invention of word processing, it was customary practice to highlight words to emphasize their importance. You may utilize underlining in your writing while being proper. These days, many writers choose to use italics as a substitute. Italics can be used to emphasize a word or a specific fact in a phrase. These are some examples of how to use emphasis: Emphasis can be added to a word or phrase by using *marks* after the text. These marks indicate that what follows is important for understanding the sentence or paragraph. There are several ways to mark emphasis with different effects. Some common techniques include italicizing, underlining, and bolding words and phrases. Italicization is the most common method of adding emphasis. It is commonly used in journalism and academic writing to draw attention to a particular word or phrase. When writing for an audience that may not be familiar with this type of formatting, using plain old italics is enough to catch readers' eyes. You can identify italicized words by looking for _marks_ after the text. Underlining is another common way of adding emphasis. Underlined words or phrases are given more weight than others when reading or listening to a document. This technique is often used by teachers and writers who want to direct students' or readers' attention to certain parts of a sentence or paragraph.

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Answer the fallowing Questions: - Explain why in C++ the function main() is a special function and why it is important. - Fill in the blanks in the following: - An error which is caught by the compiler is a ______ error. - The operator that tests for equality is _____. - The do-while statement terminates when its condition is______. - ______ is a type with no objects. - The elements of an array are related by the fact that they have the same _____ and_____. - Explain how information is passed to and returned from a function. - Given the following definition of a Swap function void swap (int x, int y) int temp = x; x = y; y = temp; What will be the value of x and y after the following call? x = 10; y = 20; - Explain what is meant by precedence and why it is important in programming, using arithmetic examples to illustrate your answer. What are the precedence rules for the arithmetic operators in C++? - Write a C++ program which produces a simple multiplication table of the following format for integers in the range 1 to 9: 1 x 1 = 1 1 x 2 = 2 9 x 9 = 81 - Explain what is meant by keyword? Give an example. - Write a function which outputs all the prime numbers between 2 and a given positive integer n: void primes ( int n ); A number is prime if it is only divisible by itself and 1. - Explain what is meant by assignment illustrating your answer with appropriate examples. - Write a function that inputs a series of 7 numbers from the keyboard into an array and then prints them to the screen with a + symbol after each number. For example if the numbers entered were 1, 4, 5, 7, 9, 30, 45, the following would be printed to the screen: These are the numbers input: 1 + 4 + 5 + 7 + 9 + 30 + 45 +

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Students will learn the characteristics of 4 different angles and use this information to identify and draw the angles. Tell students that today they will be learning about 4 different types of angles. Begin your presentation with a right angle. Demonstrate how a right angle measures 90 degrees with a protractor. Ask students to name some items in the room with a right angle. Example: the corner of a book, the corner on the window. Introduce the other angles by referring to and comparing them to the right angle. Tell students that an acute angle is smaller than a right angle, or under 90 degrees, and that an obtuse angle is wider than a right angle, or greater than 90 degrees. Tell students that when an angle measures exactly 180 degrees, it just looks like a straight line and is referred to as a straight angle. Create an anchor chart with the 4 angles that lists their characteristics. Ask the students to help you create a T-chart on the whiteboard or the document camera and write down how the angles are similar and how they are different.

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As a teacher, it is important that you are able to recognize and understand how to work with all types of students, especially those with disabilities. The goal of this training is for you to feel confident about your ability to meet the needs of each student in your classroom. After completing this training, you’ll understand what inclusive education means and recognize the benefits of inclusive education. You’ll also learn how to create an inclusive learning environment for all students, including how to modify instruction for students with special needs and how to collaborate with other teachers and parents. Inclusive education is the practice of educating ALL learners in their neighbourhood schools in age-appropriate, regular classes and providing them with the supports they need to succeed. It’s more than just placing students with diverse needs into a classroom. It’s about creating a learning environment that promotes positive relationships and equal opportunities for all students. The students who benefit most from inclusive education are those who have been excluded from school due to poverty, disability, race, gender and ethnicity. They’re at a higher risk of not receiving an adequate education because of their circumstances. This training was created for teachers who are working with students with disabilities. It will provide you with a basic understanding of disability, disability law, and give you some strategies to support students with disabilities in your general education classroom. This course will introduce you to the fundamentals of inclusive education, including inclusive practices you can use in your classroom, how to create an inclusive environment, and how to use differentiated instruction to support diverse learners. You will also learn about common disabilities and how they affect learning. Inclusive education is a program that encourages the inclusion of all children in regular classrooms during their regular school day. This type of education has the goal of creating an environment where every child, regardless of their educational needs, feels welcome and valued within the classroom. An inclusive class is not only beneficial to students with special needs, but also to students without any learning or physical disabilities. To make an inclusive classroom truly work for all students, teachers must be well-equipped with both knowledge and skills for effective teaching. Part of this teacher training course addresses the knowledge base needed for teachers to understand how to best accommodate all students’ needs in an inclusive setting. The other aspect of this training course focuses on developing the skills needed to effectively implement these accommodations so that the classroom runs smoothly and successfully. The following information will allow you to integrate your existing knowledge and skills with new strategies and techniques on how to create a positive learning environment for all students, no matter what their individual needs may be.

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Differentiation evaluates the rate of change of a function, which is the same as the gradient on a graph. A gradient on a graph is given as `frac(text(change in )y)(text(change in )x)`. A differentiation is shown as `frac(dy)(dx)` - often said as differentiate dy by dx. The process is to take a term `ax^n` >multiply the coefficient by the power< >subtract 1 from the power< Note that if there is a constant in the expression, then that constant is dropped. If `y = ax^n`, then `frac(dy)(dx) = anx^(n-1)`. If a function `f(x)` is differentiated, it is shown as `f`(x)`. A function `f(x) = ax^n` would differentiate to `f`(x) = anx^(n-1)`. The power, `n`, can be positive, negative, a fraction or a decimal. A curve has an equation of `y = 5x^3 - 7x^2 + 3x -5`. Find `frac(dy)(dx)`. For each term, multiply the coefficient by the power, and subtract 1 from the power. `5x^3` becomes `3 xx 5x^(3-1) = 15x^2` `-7x^2` becomes `2 xx -7x^(2-1) = -14x` `3x` becomes `1 xx 3x^(1-1) = 3` The contant -5 is dropped `frac(dy)(dx) = 15x^2 -14x + 3` Answer: `15x^2 - 14x + 3` A curve has the equation `y=-2x^3+4x-7`. A tangent is drawn to the curve when `x=-2`, and another tangent is drawn to the curve when `x=2`. Describe the relationship between these two tangents. The gradient can be found by differentiating the equation. `frac(dy)(dx) = 3 xx -2x^(3 - 1) + 1 xx 4x^(1-1) = -6x^2 + 4` Substitute the values of `x` from the coordinates into the equation. Both gradients are the same, therefore the lines are parallel. Answer: They are parallel. Reason: `frac(dy)(dx) = -6x^2 +4`. When `x=-2, frac(dy)(dx) = -6(-2)^2 + 4 = -20` When `x=2, frac(dy)(dx) = -6(2)^2 + 4 =-20` Both gradients are the same.

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In order to complete the meaningful sentence we must have knowledge of parts of speech along with articles and determiners. What are Determiners ? Determiners are defined as the words that are used before a noun to ‘ determine ‘ or ‘ indicate ‘ whether something specific or particular is being referred to. They comes before noun and highlights or point out them . Examples of Determiners : (a) These puppies (b) My neighbor (c) Any book (d) A man these , my , any and a are Determiners. Difference between Adjective and Determiners : (a) Spacious apartment (b) that apartment The word spacious describing the apartment .It is an Adjective , because it is describing a noun and telling about the quality of apartment. The word that does not describe the apartment but specifies the apartment , it points out a particular apartment . It is determiner. Therefore , Adjectives describes a noun and tells more about some special quality or how many whereas a A determiner points at a noun and tells which one . Types of Determiners : Determiners are of many kinds , they can be articles , demonstratives , possessives , quantifiers , distributives and interrogatives . 1) Articles : The words a, an and the are called Articles . As they are the determiners , therefore they comes before the noun. The articles , a and an are called indefinite articles while the is called the definite article. Usage of article ‘a’ : • Article ‘ a ‘ is used before singular countable nouns which begin with a consonant sound . Example : a pen , a coin , a bag • Article ‘a’ is used to show rank , community or a kind , class or species Example : a monkey , a nurse , a student • Some words begins with vowels when written but begin with consonant sound , here we use ‘a’ Example : a Union, a University Usage of article ‘an’ : • Article ‘an‘ is used before singular countable nouns which begins with a vowel sound . Example : an umpire , an elephant , an owl • Some words begins with a consonant when written but begin with a vowel sound when spoken , here we use an Example : an honour ( h of the word honour is silent here) Similarly , an MLA ( the consonant M is pronounced as em) Usage of ‘ the ‘ : • When we refers to a particular person or thing, unique things , famous , brands or certain group of words. • The boy laughed. • lets go to the Talkies. •The Burj khalifa is tallest building in world. • the east , the rich , etc. The words like this , that , these and those which out to persons or objects close by or at a distance are called Demonstratives. For example : (a) This Table is not furnished well. (b) That building has twenty five floors . 3) Possessives : Possessive adjectives that show someone’s possession such as my , her , his , it’s , their and our , are called Possessives . Since they are the kind of Determiners therefore they are used before noun. Examples : my sister , his name , her husband 4) Quantifiers : Those determines which tells us something about the number or quantity are called as Quantifiers . (a) Words such as much , many , a few , most , cardinal numbers ( one , two , three) and none . (b) many gems , several plants , much sorrow, some advice . 5) Distributives : Those Determiners that show distribution are called Distributes . Examples : Words like either, neither , each and every . • Each is used with a singular verb when limited number of persons are considered individually with emphasis on the individual. • Every is used with singular verb when a large number of persons or things are considered individually. • Either is used with a singular verb meaning anyone of the two or each of two. • Neither is used with a singular verb meaning not one or the other. (a) Each player of basketball team played his best. (b) Every student must bring their Sports kit tomorrow. (c) You can take either of the pen. (d) Neither book explains the concepts of quantum mechanics in detail.

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Earthquakes occur along the plate boundaries; however, the exact location of an earthquake is determined by using seismographs. A seismograph is an instrument used by the scientists (known as seismologists) to record an earthquake. A seismogram is the recording made by a seismograph. The seismograph consists of a mass which is attached to a fixed base. When the earthquake occurs, the base shakes along with the ground. On the other hand, the string to which the mass is attached absorbs the movement and ensures that the mass stays fixed. This relative motion of the base with respect to the mass is recorded. Interestingly, a seismograph can only tell how far away an earthquake occurred and not its directions. Scientists use a set of three seismographs to determine the exact location of an earthquake through a process called triangulation. Using each seismograph, scientists can draw a circle whose radius is equal to the distance of that seismograph from the earthquake. The point of intersection of three such circles (recorded by three independent seismographs) will give us the exact location of an earthquake. I hope this helps.

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In workshop 3 we saw an example, where we created a list by starting with an empty list and using a loop to repeatedly append items to our list. Here we are going to do the same to loop over a string and build a new string. First we need to see how we can loop over a string easily. Let's examine this code: s = "fun" for ch in s: print(ch) f u n This is similar to the for item in list loop that we used in the workshop. The loop body executes three times (once for each letter in string s) and the variable ch becomes the next letter in s on each pass of the loop. And we can use the variable ch in the body of the loop. Let's do something more interesting with ch than just print it. Let's build another string where we replace all the original = 'looping over strings' result = '' for ch in original: if ch == 'o': result = result + '*' else: result = result + ch print(result) l**ping *ver strings Remember that we can use the + operator (the plus sign) to concatenate strings. Let's do one more example, where we write a function to reverse a string. def reverse(original): ''' (str) -> (str) Return a string that is the reverse of original. >>>('Forward') 'drawroF' ''' result = '' for ch in original: result = ch + result return result And call it on a couple of examples. print(reverse('Forward')) print(reverse('abc 123')) drawroF 321 cba Notice that inside the loop body, we concatenated ch to the front end of result. This week's homework will give you practice looping over both strings and lists using both the for item in X and the for i in range(len(X)) loops.

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Black History Month Profile: Rosa Parks With her family support, activism, and determination, Rosa Parks is thought to be one of the most iconic figures of the civil rights movement. Her infamous actions onboard a bus in Alabama, sparked new laws and changed the face of segregation across the country. Parks was born in 1913 and was raised by her mother and her grandparents. They were living under the rules of segregation in the south, something Parks said she was determined to help change. In 1945, she became a leader in the fight for desegregation, taking a position as the secretary of the Montgomery, Alabama branch of the NAACP. While there, she helped with black voter registration, youth outreach, and legal representation for black victims of white brutality. She held this position for 10 years until her infamous stand on board a bus in Alabama. Parks was on a bus in Montgomery on December 1, 1955, when she was asked to give up her seat for a white man. This was part of the segregation law in Alabama at the time. Parks refused to give up her seat and was arrested. She later said she knew this was likely to happen, but she was ready to accept the consequences. However, as a result, the community stepped up to show their support and organized a bus boycott which lasted about a year. Due to the lack of ridership, the bus company was forced to shut down 13 months later. “I did not want to be mistreated, I did not want to be deprived of a seat that I had paid for. It was just time… there was an opportunity for me to take a stand to express the way I felt about being treated in that manner. I had not planned to get arrested. I had plenty to do without having to end up in jail. But when I had to face that decision, I didn’t hesitate to do so because I felt that we had endured that too long. The more we gave in, the more we complied with that kind of treatment, the more oppressive it became.” After the bus boycott, Parks and her family moved to Detroit and worked with congressman John Conyers, helping to find housing for the homeless. She also remained an active member of the NAACP. Parks has received many honors for her actions promoting the civil rights movement. In 1999, Parks was given the Congressional Gold Medal of Honor, the highest honor a civilian can get in the U.S. Parks’ legacy is cemented in the history of the United States, and many have called her “the first lady of civil rights.” Her lasting impact is still being felt today.

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The diagram shows a point P that one of the three light rays A, B, and C might possibly pass through after being reflected. Which light ray would pass through the point? (A) Ray A, (B) ray B, (C) ray C, (D) all of these rays. The question is asking us to work out which of the three rays, A, B, or C, passes through point P after reflecting off the surface shown in the diagram. Let’s recall that in the absence of anything in the way, light rays travel in straight lines. We see though that, in this case, there is something in the way of these light rays. Specifically, there’s this surface right here, which the light rays will reflect off. We can see that this surface is not flat. Reflection off an uneven surface like this is known as diffuse reflection. We can recall that the law of reflection tells us what happens to light rays reflecting off a surface. First, we’ll consider a flat surface. We can draw in a line perpendicular to it, which is known as the normal line or the normal to the surface. Let’s suppose that we have an incident light ray that makes an angle of 𝜃 sub i to this normal line. This is the angle of incidence of the light ray. The ray will be reflected from the surface according to the law of reflection, which says that the angle of reflection is equal to the angle of incidence but on the opposite side of the normal. The angle of reflection, which we’ll call 𝜃 sub r, is the angle that the reflected light ray makes to the normal line, that is, this angle here. So, the law of reflection says that 𝜃 sub i is equal to 𝜃 sub r. We have to be careful applying this law when we have diffuse reflection from an uneven surface. Because the surface is uneven, the direction of the normal line will not be the same at all points on the surface. In this case, for each incident light ray, we need to take care to draw in the normal line in the direction perpendicular to the particular part of the surface that the light ray hits. Let’s now use this information to extend the path of each of these three light rays from the question. We’ll begin with ray A. We know it travels in a straight line until it meets the surface. Then, we need to draw in the normal line at the point where the ray hits the surface. That normal line looks like this. We know from the law of reflection that the angle between the normal and the reflected ray is equal to this angle here, between the incident ray and the normal. Measuring this angle and drawing in the reflected ray at this same angle, we see that ray A does pass through point P. Now, we need to see whether or not rays B and C also pass through this point P. We’ll use the exact same process to find the path of the reflected rays as we just used for ray A. Extending rays B and C until they meet the surface, drawing in the normal to the surface at each point, and applying the law of reflection, we have the path of the reflected rays for light rays B and C. Ray B ends up reflected such that it hits the surface again at this point, while ray C ends up over here. So, neither of the reflected rays B and C pass through point P. The only one that does is ray A. So, the correct answer here is given in option (A). The only light ray that passes through the point marked P is ray A.

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Over the hundreds of millions of years trees have been present on Earth, they have survived a variety of circumstances. Changes to climate conditions such as temperature and precipitation through time caused tree species to evolve in a variety of different ways, and one of the most visible examples of these adaptations is their leaf type. The two most common categories of leaves are broad and needle, and each has specific advantages. Universally, leaves have a few crucial responsibilities to help trees survive: they absorb carbon dioxide and sunlight to help fuel photosynthesis, release oxygen back into the atmosphere, and they provide food and homes for many kinds of animals and insects. All types of leaves contain a substance called chlorophyll, which absorbs energy from light during photosynthesis and gives leaves their green color. Other than their functions, though, types of leaves are more different than they are similar. Broadleaf trees have wide, flat foliage, which is discarded if the weather gets colder. They are often deciduous—in autumn, colder temperatures cause the chlorophyll in broadleaf trees to break down, making them lose their green color and eventually fall. Some broadleaf trees live in temperate and tropical areas of the world, where the soil contains enough nutrients for the trees to produce new leaves each spring. This means in hot, humid environments such as the Amazon, broadleaf trees are never met with the low temperatures that cause all their leaves to fall at once, though some lose leaves in accordance with the wet-dry cycle. Broadleaf trees also improve forest growth and increase biodiversity in their ecosystems. Needleleaf trees, also called conifers, are most prevalent in colder, high-latitude and high-altitude environments. They evolved during a period of history about 250 million years ago, when Earth was much colder and drier. Generally, their leaves remain on the tree year-round despite the changing seasons. The long, thin leaves are more adept at retaining water than broad, flat ones, and are less likely to be damaged by the wind. Since needles do not fall off the tree annually, they can also keep performing their responsibilities for the tree year-round as conditions allow. Needleleaf forests in boreal areas also act as an enormous carbon sink, absorbing greenhouse gasses from the atmosphere and storing it. The phenology of broad and needleleaf trees, or their seasonal patterns and changes, have exceptions in certain species. Some conifers like the tamarack and larch are deciduous, and their needles turn reddish-orange and fall to the ground when temperatures drop. A number of species in the genus Quercus are referred to as “live oaks” because they remain green and alive through the winter, while other oaks lose their foliage. This map layer shows the geographic distribution of broadleaf, needleleaf, and mixed-tree forests, and was created using a model that combined multiple datasets. The intensity of each color on the map layer represents the consensus prevalence, or the amount that all the different datasets agree―in other words, the darker the color, the more certain it is that a certain leaf type exists there. You can clearly see the broadleaf trees dominating the Amazon rainforest, as well as needleleaf forests spanning Canada, Russia, and the Scandinavian Peninsula. Compare this map layer to the Biomes, Surface Air Temperature, and Precipitation layers to see how leaf types are influenced by climate. Forests are important parts of the natural world that protect us from more extreme effects of climate change, provide us with materials like timber, support global biodiversity, participate in the water and carbon cycles, and much more. However, things like logging, insect damage, disease, and fires threaten the health of these crucial ecosystems. There are many organizations that aim to protect forests from these hazards, from local groups to the United Nations and at every scale in between. To get involved with forest conservation, try searching the internet for opportunities near you.

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Pattern Worksheets For Class 3 Pattern recognition and creation are crucial skills that young learners need to develop in order to build a strong foundation in mathematics. Pattern worksheets for class 3 are designed to help students in their third year of primary education understand the concept of patterns and enhance their analytical and problem-solving abilities. Pattern worksheets for grade 3 are designed to teach children how to recognize, extend, and create patterns. These worksheets may include exercises that require students to identify and complete patterns, as well as activities that encourage them to create their own unique patterns. Students may also be asked to continue patterns by identifying the rule that governs the sequence of numbers, shapes, or colours. At HP HP Print Learn Center, our pattern worksheets for class 3 include a range of exercises that challenge students to identify, extend, and create patterns. Some of the exercises that may be included in our pattern worksheets for class 3 are: Completing Patterns: Students are presented with incomplete patterns and are required to identify the rule and fill in the missing elements. Example: Fill in the missing elements: 10, 20, 30, ____, 50 Creating Patterns: Students are given a set of numbers or shapes and are asked to create their own unique pattern. Example: Create a pattern using the numbers 5, 10, and 15. Identifying the Next Element: Students are presented with a sequence of numbers or shapes and are asked to identify the next element in the pattern. Example: What is the next number in the sequence: 2, 4, 6, 8, ____? Our class 3 pattern worksheets include a range of exercises that are designed to encourage students to think creatively and develop strong analytical skills. In addition to our Maths worksheets, you can also watch videos on our YouTube channel that include tips and strategies for teaching maths, as well as interactive activities and games that are designed to engage and challenge students.

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During Progressive Era, there were many reforms that occurred, such as Child Labor Reform or Pure Food and Drug Act. Women Suffrage Movement was the last remarkable reform, and it was fighting about the right of women to vote, which was basically about women’s right movement. Many great leaders – Elizabeth Cad Stanton and Susan B. Anthony - formed the National American Women Suffrage Association (NAWSA). Although those influential leaders faced hardship during this movement, they never gave up and kept trying their best. This movement was occurred in New York that has a huge impact on the whole United States. Before the Women’s Suffrage Movement started, women didn’t have many rights. African-American women and slaves had less rights. They didn’t have legal protection; some didn’t even get the right to raise their own child. Other women had more rights, but not as many as men. They weren’t able to go to college, they had to work at home, weren’t allowed to have strong public opinions, some were sold or even forced into marriage so their family could get more money. It was a slow-developing but nation-wide movement led by women, produced the Women Suffrage Movement and eventually, the right to vote. One good thing about being an American is everyone’s right to vote. For Women prior to the 1920’s that was not the case. A woman’s right to vote would have to be passed into law under the 19th Amendment to the United States Constitution. The 19th Amendment was introduced to Congress in 1878, but was not ratified until 1920 (National Achieves). For over 40 years women would have to rally together and publicly protest just for the right to vote. Women protesting and speaking out was considered very unladylike at the time (Rampton). This hard earned victory proved what women can do when organized and became a chronological landmark for the beginning of Women’s Liberation Six well-bred women stood before a judge in the Washington D.C. police court on June 27, 1917. Not thieves, not drunks, not prostitutes, like the usual attendants there. They included a university student, an author of nursing books, a prominent campaign organizer, and 2 former school teachers. All were educated accomplished and unacquainted with criminal activity, but on that day they stood in a court of law with their alleged offense, “Obstructing traffic”. What they had actually done was stand quietly in front of the White House holding banners, urging president Woodrow Wilson to add one sentence to the constitution: “The right of citizens of the United States to vote shall not be denied or abridged by the United States or by any account of sex”. The debate over Women’s Suffrage stretched from the mid 1800’s to the early 1900’s, as women struggled to gain a voice in politics. At the beginning of the nineteenth century, American society began to focus on the welfare of minority groups. Women’s suffrage and abolition were rooted as deeply as the history of America, but asylum and prison reform sprouted with the Second Great Awakening, a movement that occurred in the early 1800s. The Second Great Awakening was led by religious leaders who advocated for changes in American society through the unity of the American people (Doc. Due to the Second Great Awakening, reform movements were established between 1825 and 1850 in order to represent the changes the people sought for in the issues of slavery, suffrage, and asylum and prison reform. The social aspect of the abolition movement led to the visible democratic changes in society and politics. For decade women have been discriminated by society, all around the world. In many countries women are still treated as the inferior sex. “daily life for women in the early 1800s in Europe(Britain), was that of many obligations and few choices. Some even compare the conditions of women in time as a form of slavery.” (Smith, Kelley. "Lives of Women in the Early 1800s." Lives of Women in the Early 1800s. N.p., 2002.) Women have always been expected to find a husband, get marry and have children and nothing less was expected of them. Women during decades ago and even today in 2017, many women live by the norm that if you don’t get marry you’re a dishonor/disgrace to the family. Many men treated women as objects and without a doubt not as equals. The impact women’s right to vote had on economic growth in the U.S, as women in integrated into the labour force from the 1920’s to the 1990’s. Have you ever thought about women 's rights and equality? It’s not as pretty or memorable as you think it is. But just like Shirley Chisholm said “at present, our country need’s womens idealism and determination, perhaps more in politics than anywhere else.” Which is true but back then it certainly wasn’t. Let me take you way back to when women and men were not equal, and when men had more power over women. Although feminism continues to be non-monolithic and contentious, it has made several progress and created new worlds of possibility for working women, education, empowerment and even arts. For many, feminist movement is about giving women liberty, equal opportunity and control over their own destiny. Suffrage means to have the right to vote in political elections. This concept is an ideal meaning for women throughout history, especially for the women population between late 1800’s and early 1900’s. Women suffrage commenced at the Seneca Falls, which later on had escalated to Unions, then led to the 15th and 19th amendment. Of course, the men of that time had belittled the women who believed that they were more than merely the traditional mothers and wives. Although, suffrage is not only just for females, but to the Black population too; both males and females. With determination and the passion burning within them, women and African Americans alike, had reached the right for suffrage. The 1960-70’s was the height of the Civil Rights Movement. African Americans were dedicated to gaining liberties which only whites could exercise freely, and did this was done through peaceful as well as violent means of protest. Individuals such as Martin Luther King protested by means of preaching peace and utilizing nonviolent actions against whites while others such as Malcolm x and elijah muhammad resorted to not only violence, yet separatism to protest and show their urge to gain civil Liberties. Though, both methods of protest were aimed towards the same goal, only one was to be influential and bring about the change that African Americans desire. This movement not only involved with white suffragists, but also with the black suffragists; the whole event was concentrating on sex and racial equality. The woman’s suffrage movement of the 1800s and early 1900s as well as the civil rights movements of the 1950s and the 1960s, even though they were made up of a multi-ethnic group of people, the two movements actually had multiple of similarities such as the same goals and concerns. Both group felt appressed by society and both groups demanded basic freedoms and equal opportunities. As both groups sough to have their demand met, other issues became the major national focus. Women in Latin America were viewed as the stereotypical housewives, as their only duty was to take care of their household and children. Their purpose in life was to direct man on the path of virtue and purify his soul with love. Latin men viewed women as the weaker sex. This was all due to the effect of Spanish colonialism of how men viewed women in Latin America. Under the Catholic Church rule, women had to be pure and accept the life that was chosen and given to them just like the Virgin Mary. Women are expected to be good wives and mothers, which typically includes self-sacrifice and putting one’s family and its survival above all else . Also, not only did Spanish colonialism influence the way women are viewed in Latin America, but it also helped rise up of women’s right in Latin America. However, the newly independent of Latin American citizens were not yet given full rights, including the women. By the beginning of the twentieth century, the suffragette movement began to break out in all over the world due to European and American influence. Women in Latin America were suppressed, and they had enough of it. They sought greater personal freedom, opportunities, and equal rights between both sexes. In this essay, I argue that women in Latin America did not have any rights, which made them sympathetic and want to follow women suffrage ideas from the United States and Europe that was already happening. The Suffragette movement Following the Gilded Age in the United States, (U.S.) where prices were high, working salary was low, political corruption was everywhere, child labor was brutal and women were suffering, came the period in history called the Progressive Era. The Progressive Era was a period of social activism and political reform that grew immensely from the 1890s to the 1920s to fix these problems. Although not every part of this progressive movement made big impacts, reformers and the federal government were mildly successful in bringing reform at a national level to correct some injustices such as working conditions, political corruption, child labor laws and women 's suffrage in American life.

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- The Constitution (First Amendment) Act, 1951 was passed by the Indian Parliament on June 18, 1951. - Several changes were introduced to the Constitution through this amendment. Fundamental rights clauses were amended and restrictions on freedom of speech and expression were provided. The amendment also encouraged the abolishment of the Zamindari system which prevailed back then. It held that the right to equality doesn’t prevent the government from making laws for the protection of weaker sections of society. - The First Amendment was enacted in response to the landmark case, State of Madras v. Champakam Dorairajan (1951). - Brij Bhushan v State of Delhi (1950) and Romesh Thappar v State of Madras (1950) are two other judgments that heavily prompted the first amendment to the Constitution. "Political democracy cannot last unless there lies at the base of...social democracy. What does social democracy mean? It means a way of life which recognizes liberty, equality, and fraternity as the principles of life..." – BR Ambedkar The Indian Constitution is the framework that outlines the structure, powers, and procedures of government and defines citizens' rights, duties, and liberties. It came into force on 26 January 1950. One of the salient features of the Indian Constitution is its combination of rigidity and flexibility. The amendment procedures are specific and stiff in a rigid constitution, whereas in a flexible constitution, amendments can be made in the same manner as ordinary laws. Indian constitution is an exceptional blend of both. On June 18, 1951, the parliament of India passed The Constitution (First Amendment) Act, 1951 which was put forth by a motion by Jawaharlal Nehru on May 10, 1951. This article seeks to understand the circumstances that led to the 1st amendment's passing, along with the substantial changes it introduced. BACKGROUND OF THE FIRST AMENDMENT A chain of events led to the passing of the 1st amendment to our constitution. State of Madras v. Champakam Dorairajan [AIR 1951 SC 226] is the first landmark judgment regarding reservations, and the first amendment was made in response to this judgment. In this case, a communal order issued by the province of Madras in the 1950s, allowed a person to admit to any government educational institution or employment. This was based on caste reservation. Even after independence, the Madras government enforced the communal order because it was established under Article 46 of the directive principles of state policy to enhance the education of weaker classes of society. Shrimathi Champakam Dorairajan challenged this system, as she could not get admitted to a medical college despite her qualifying marks since she was a Brahmin. In this historic judgment, it was held that the reservation system violates Article 29(2) of the constitution and that fundamental rights will always prevail whenever there exists a conflict between the DPSP and fundamental rights. The communal order was struck down by Madras High Court as it was against the constitution. This judgment led the parliament to modify any laws that conflicted with the DPSP through the First Amendment. Press freedom in the 1950s was another paramount factor that influenced the government to amend the Constitution. The government faced heavy criticism and backlash from the media, owing to events such as extra-judicial killings of communists in Madras, refugee inflow in West Bengal, etc. The government deemed it vital to suppress the rights and freedom of the press. Romesh Thapar v State of Madras [(1950) S.C.R. 594] is one of the earliest cases regarding freedom of the press in India. In this case, Mr. Thapar published weekly articles voicing his personal opinions and skepticism regarding Jawaharlal Nehru’s policies in the magazine "Crossroads". In March 1950, the Government of Madras prohibited the circulation of this magazine in certain areas. The ban was imposed according to Section 9(1-A) of the Madras Maintenance of Public Order Act, 1949 that granted power to the government to prohibit the circulation, sale, or distribution of the journal for ‘public safety’ or preserving ‘public order.’ Mr. Thapar approached the supreme court of India, arguing that the action of the Madras government was infringing his fundamental rights. The Supreme Court defined the terms “public safety” and “public order”, and tested whether they fall under the reasonable restrictions given in Article 19 (2) of the Constitution. The court held the government order unconstitutional as it infringed on freedom of speech and expression. In the landmark case of Brij Bhushan vs. the State of Delhi [(1950) SCR 605], the Supreme Court ruled that freedom of speech and expression is a fundamental right that the state cannot suppress unless it incites violence or amounts to defamation. The press has the right to criticize government and officials as long as it is done reasonably and decently. CHANGES INTRODUCED BY THE AMENDMENT - First Amendment to the constitution amended Articles 15, 19, 85, 87, 174, 176, 341, 342, 372 and 376. - Clause (4) was added to Article 15 which acted as a non-discrimination clause. It empowered the government to make laws for the upliftment of the backward classes. - Clause (2) of Article 19 was altered. It provided reasonable restrictions against the right to freedom of speech and expression under Article 19(1)(a). - Ninth Schedule was inserted into the constitution which excluded all laws from the scope of judicial review. Currently, 284 Acts are included in the ninth schedule which cannot be challenged. - Article 31A and Article 31B were inserted into the constitution. Article 31A provided that five categories of laws would be saved from being invalidated because they were against the guaranteed fundamental rights of the Constitution. However, in the case of I.R. Coelho (dead) by L.Rs. v. State of Tamil Nadu and others [(1999) 7 SCC 580], the supreme court ruled that even the laws under the ninth schedule will be subject to judicial scrutiny if it is against the constitution or its basic structure. - Article 85 and Article 174 were modified to include provisions related to Parliament/ State Legislature sessions, prorogation, and dissolution. - Article 87 and Article 176 were modified to change the occasions where special addresses should be made by the President/Governor. - Articles 341 and 342 were amended to empower the President to specify castes, races, and tribes concerning any state. - Clause (2) was inserted into Article 372 which gave the President the power to modify the existing laws for a certain period after the commencement of the Constitution. - Article 376 was amended to provide that High Court judges of any province can be eligible for appointment as Chief Justices of High Courts. The first amendment to the Constitution has unceasingly been the topic of many debates and discussions. The ninth schedule, which exempts all the laws included in it from judicial review, has been conceived as controversial due to its blatant misuse. In November 2022, the supreme court of India agreed to hear a Public Interest Litigation (PIL) that challenged the changes brought about by the First Amendment Act, of 1951. The examination of reasonable restrictions given under Article 19(2) is the primary subject of the petition Join LAWyersClubIndia's network for daily News Updates, Judgment Summaries, Articles, Forum Threads, Online Law Courses, and MUCH MORE!!"

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A _______________ is mathematical rule that assigns each input exactly one _______________. Functions can be represented as a set of ordered pairs, a table, a graph or When a function is written as a set or ordered pairs or a table, there can be no repeats in the x value/_______________. If there is a repeat in the x value, then it is not a _______________. When looking at a graph, you can use the _______________ to determine if the graph makes a function. When you draw a vertical line, it should only hit the graph one time. If the line you drew hits the graph more than once, it is not a _______________. Functions can be _______________ or non-linear. If a function is linear, that means there is a constant rate of change. If the function is written as a table, you should look for a constant change in the _______________ and a constant change in the outputs. If there is a constant change, then the table is _______________. If a function is on a graph, it has to be a straight line in order to be _______________. If it’s not a straight line, then it’s not linear. When written as an equation, there are a couple things to look for that will make it non-linear. First, the variables can’t have any exponents. Second, the variables can be multiplied together. If the variables don’t have exponents and they aren’t being multiplied together, then the equation is _______________.

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Vocabulary is vital in improving language skills as it allows individuals to effectively express their thoughts and ideas. Vocabulary Workshop Level D Unit 3 aims to broaden students’ vocabulary by introducing new words and their meanings. This article provides answers, explanations, and examples for Unit 3 to support students in enhancing their language proficiency. Vocabulary Workshop Level D Unit 3 Answers: Enhancing Language Skills 1. Synonyms and Antonyms In this section, students find synonyms and antonyms for words. This helps them understand word relationships and expand their vocabulary. For instance, a question might ask for a synonym for “amiable,” with the correct response being “affable” or “friendly.” Similarly, students might be asked to identify an antonym for “assertive,” with the correct answer being “submissive” or “passive.” This practice improves word choice and communication skills. 2. Completing Sentences Students fill in the blanks in sentences using vocabulary words to improve sentence construction and contextual understanding. For example, a sentence may require selecting the appropriate word to fill the blank, such as “The chef’s __ in the kitchen was evident as he prepared the gourmet meal.” This exercise reinforces vocabulary comprehension and usage. 3. Choosing the Right Word Students are given sentences with bolded words and must choose the correct word to replace it. This helps them improve their understanding of word usage and choosing the right word in different contexts. For example, a sentence may say: “The ___ of the crime was unknown to investigators.” Students would choose “perpetrator” as the replacement word. Vocabulary Workshop Level D Unit 3 answers aid students in improving language skills by teaching them how to use words correctly. By identifying synonyms and antonyms, completing sentences, and selecting the appropriate word, students can expand their vocabulary, enhance sentence construction, and grasp word meanings. Regular practice with vocabulary exercises can improve communication skills in both writing and speaking.

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Introduce the concept of vertical farming to the children by showing them a short video about it (https://www.youtube.com/watch?v=vhJA7Zu8B3I). Explain to them the benefits of vertical farming in terms of sustainability, efficiency and safety. Talk about how vertical farming solutions support environmental sustainability in terms of reducing wastage, minimising land resources needed, and promoting safe and sustainable food production. 1) Explain what vertical farming is and why it’s important in terms of sustainability. 2) Show a video of a vertical farm (https://www.youtube.com/watch?v=5KTzS-y0XgY) 3) Break the children into groups and give each group a task to research different vertical farms around the world. They can look into the different types of vertical farms and the impact they are having on the environment. 4) Ask the children to draw a diagram of a vertical farm and label the different parts and features. 5) Invite a representative from a local vertical farm to come in and give a short talk about their experiences and the impact vertical farming has had on sustainability. 6) Ask the groups to present their findings to the whole class. Encourage them to think of creative solutions to global environmental problems that vertical farming could help to solve. 7) Ask the children to write a creative piece of writing or poem about vertical farming, or create a picture or poster that promotes the idea of vertical farming to others. Throughout the lesson, ensure to ask the children open-ended exploratory questions to ensure they are engaging with the content of the lesson, e.g. “What do you think are the advantages of vertical farming?”, “What kind of environmental problems do you think vertical farming could help with?” Observe the children throughout the lesson, as well as their groupwork and presentations, in order to assess their understanding and engagement. Use this observation to provide feedback and support for the groups. Provide additional resources for the more able children, such as an article about the latest developments in vertical farming (https://www.bbc.co.uk/news/technology-49243023). Allow time for the less able children to discuss the concept with their peers to better understand it before they are asked to create their pieces of work. Provide two versions of the creative pieces of work – one which allows for drawings and colours, and one which allows for more descriptive writing. Invite the children to discuss the concept of vertical farming and the impact it has on environmental sustainability. Ask them to think of suitability, cost, and other potential benefits and drawbacks of vertical farming, and how it fits into the wider context of environmental sustainability. - Video: https://www.youtube.com/watch?v=vhJA7Zu8B3I - Video: https://www.youtube.com/watch?v=5KTzS-y0XgY - Article: https://www.bbc.co.uk/news/technology-49243023 - Worksheet: https://www.twinkl.co.uk/resource/t-t-53119-vertical-farming-activity-sheet

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A skit is a short performance in which the actors make fun of people, events, and types of literature by imitating Skits are a clever way to get students to teach one another without lecturing or reading a report. Students can role-play different situations, and those watching can respond afterward with critiques and further discussion. 4. Characteristics Involved and Developed through Classroom Skits Individual Accountability: Students are each responsible for a specific part of the skit production, and to contribute to other parts as needed. If they do not perform their individual job, or contribute to other tasks, then the skit will not come together as a whole. Positive Interdependence: Students work together and rely on the other members to produce a skit. Each student may have a specific job, but the students must communicate with one another, and eventually the students must pull all of their parts together: to read the play, practice parts, set up the props, and put on the production. A single student is not responsible for the entire production. 5. Social Skills: Students are required to work together, which means that they must communicate with one another and spend Face-to-Face Interaction: Students are working as a group to develop a skit. They must talk to one another in order to develop all of the separate parts. They must also practice the skit, so they will be required to practice their individual parts in front of one another. Open Communication: Students must talk to one another and discuss their ideas for the skit, problems they may be having, and how the progress is going on each of their individual parts. Open communication, in turn, builds trust and security because students must trust their group members and feel safe in order to express ideas and opinions. Shared Goals: Students work together on one project. Although each member has his or her own part, each job is a small part of the larger project. The students all have the same end goal of putting on a skit for their class. Costumes and props will likely be needed for this lesson, depending on the students’ skits. Students can adapt costumes from a costume box for their skit or they may use materials/clothes from home to make their own costumes. Elaborate costumes are not necessary. Students can make their own props and can recycle materials such as boxes and paper scraps to do so. If all materials for costumes and props come from the classroom or home, there should be no cost. 1. Divide students into groups. If working with a variety of age/grade levels, divide groups so that there are equal numbers of the different age/grade levels in each group. In other words do not have all fifth graders in one group and all third graders in another group. It is beneficial for varying age levels to work together, so that they can learn to get along with and work with someone older or younger than 2. Either assign students to jobs with in their group related to the production of the skit or have the students pick their own jobs. The students’ jobs should be related to their talents and/or interests. 8. Examples of jobs and their 9. 3.Teachers may either provide students with a story to act out or they can have the students write their own skits. 4. Decide on a day and time for the acting out of the skits. Provide a stage area for the students to perform. It is also fun for the students if the area in which the performances will occur is set up like a theater and if “tickets” are “sold” and required for entry into the play(s). Rows of chairs can be set up facing the stage area in order to simulate a theater atmosphere. 5. Finally, have the children perform their skits. The skits can be acted out just for their class or other classrooms can be invited in to watch. 10. HOW TO MAKE A SKIT Developing an Idea Writing Your Skit Performing or Filming Your Skit

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Strategies are listed from the earliest strategies up through the standard algorithm. Many are used side by side, but it is important to understand that the variety of strategies are used to build a deeper conceptual understanding and move to a more procedural model backed by conceptual understanding of division. Keep in mind that mastery of the standard algorithm of division is not expected until grade 6 per the Maine Learning Results and Common Core State Standards, however students will begin practicing the standard algorithm along side other strategies much earlier than grade 6. Using models for division are going to be important to help students understand what division represents. The context of a division problem is going to be helpful in selecting an appropriate strategy and model and the context will also help students understand what to do with any remainders - can the remainders be broken up equally, left as remainders, or do you have to do something else. Most of the strategies below are using a model to solve division problems, so specific information about each model will be given there. As a reminder, to build flexibility in understanding division and strategies, students need practice with missing dividends, missing divisors, and missing quotients. These different types of problems should be introduced at different times within their learning progression. For more information about varying the types of division word problems students should use, check out the Glossary Table 2 from the Common Core State Standards for Mathematics. When beginning to learn about division, we often refer to equal groups or fair shares. Students can physically act out sharing a variety of manipulatives as they make small groups or make equal groups of a certain size. This is where the context of the problem is important. This strategy is also referred to as repeated subtraction because you are taking away each group or one for each group as you equally share. Much like equal groups, using arrays is a way to visualize an organized arrangement to see equal rows. Using this strategy, students would create rows the length of the divisor and see how many rows they could create. Once created, the array model shows the rows and columns representing the quotient and divisor with a total amount of objects representing the dividend. Watch the quick video to see how manipulatives can be used to create the array for division. Area Models (Connects to Multiplication) The area model can be a great strategy for modeling division with small or large numbers. It can easily transition to decimals as well. This strategy also connects well to the area model strategy for multiplication and shows how the two operations are related. In the area model, students start with a rectangular are model with the divisor listed on one side as one of the dimension of the rectangle. The student can then use break out pieces of the model to show smaller chunks of the dividend, using facts they know or are easier to use. The process continues until the entire dividend value is reached. The quotient is then the total of all the lengths on the side of the rectangle adjacent to the divisor. This strategy is great for large numbers that are harder to model with manipulatives. Watch the video for several demonstrations of this strategy in action. The partial quotient strategy utilizes facts that students know and often connects to place value. It is similar to the standard algorithm, however students can use the divisor and break out small partial quotients and work toward the final quotient. This strategy can rely on any facts, however most students use multiples of 2, 5, 10, or 100 to help them successfully divide out smaller partial quotients. As students become stronger with this strategy, they become more efficient with their partial quotients. For a detailed example of how this strategy can work in several ways, please watch the video below. US Standard Algorithm The US Standard Algorithm is the strategy most people think of when they hear long division. It probably also creates a bit of anxiety for some people. The standard algorithm for division is a set of procedural steps that when followed correctly can give you a quotient, but there is rarely understanding or meaning behind the steps. There are even several mnemonic device strategies that you may have learned as a student to help you remember the steps. We want students to have a more conceptual understanding of division, so these procedural steps need other strategies (from above) to support what is happening beyond just following a list of step. The partial quotient strategy is a great stepping stone to the standard algorithm. Graham Fletcher Video - Progression of Division

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What our Modal Auxiliary Verbs lesson plan includes Lesson Objectives and Overview: Modal Auxiliary Verbs teaches students about modal auxiliary verbs and how to use them in their writing. At the end of the lesson, students will be able to use modal auxiliaries (e.g., can, may, must) to convey various conditions. This lesson is for students in 4th 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 green 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 supplies you will need for this lesson are scissors, containers, and the handouts. 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. A few of the suggested adjustments are for the lesson activity. For the activity, students can write the sentences on a separate sheet of paper. They can also switch partners once or twice during the activity. For an additional lesson activity, you can have your students write a short story using each of the modal auxiliary verbs at least once. You can also have your students identify the use of modal auxiliary verbs in their current reading or other subject content. Finally, you can conduct a “Modal Auxiliary Verb Bee” where students correct sentences that use modal auxiliary verbs incorrectly by changing the sentence or the verb. The teacher notes page includes a paragraph with additional guidelines and things to think about as you begin to plan your lesson. This page also includes lines that you can use to add your own notes as you’re preparing for this lesson. MODAL AUXILIARY VERBS LESSON PLAN CONTENT PAGES What is a Modal Auxiliary Verb? The Modal Auxiliary Verbs lesson plan includes three content pages. Students have likely already learned about auxiliary verbs, also known as helping verbs. Some examples of helping verbs include have and are. We can use auxiliary verbs as linking verbs alone or with an action verb. They can express time relationships and moods. They can also form the tense and voices of other verbs. We can use the helping verb is/has as a linking verb, in sentences like: Maria is tall. My friend has a game after school. We can also use is/has with action verbs: Tony is running home. My mom has arrived home. Some common auxiliary verbs include be, do, and have verbs. Be verbs include am, is, are, was, were, being, and been. Do verbs include does, do, and did. Have verbs include has, have, had, and having. Another type of auxiliary verb is the modal auxiliary verb. These don’t change form, and you can’t add an ed, ing, or s ending to them. Modal auxiliary verbs indicate necessity or obligation, possibility, willingness, or ability. They include can, could, may, might, must, ought to, shall, should, will, and would. Using Modal Auxiliary Verbs You can use modal auxiliary verbs with action verbs and other helping verbs, just like auxiliary or helping verbs. Modal auxiliary verbs show necessity, obligation, possibility, willingness, or ability. The lesson shows each of these uses with example sentences that show how you can use modal auxiliary verbs. To show necessity or obligation, you might use a modal auxiliary verb in the following ways: You should wake earlier each day if you do not want to be late for school. You must remember to do your homework each night. Noah ought to be studying more often if he expects to get an A on the test. To show possibility, you might use a modal auxiliary verb in the following ways: Chloe might visit you on Saturday if she is available. Because he was so hungry, I think Jason could have eaten another whole pizza. The weather forecaster said it may rain tomorrow. To show willingness or ability, you might use a modal auxiliary verb in the following ways: Sean will mow the lawn this Saturday for a reasonable price. I think you can swim much faster if you practice every day. Kimberly thought she would sing well during the concert at the school, and her mother agreed. You can use modal auxiliary verbs in certain patterns, including modal + main verb (I may eat a hamburger and some French fries for dinner), modal + be + present verb (You should be studying for the test and not be playing games), and modal + have + past verb (Molly may have completed the work, but there is more to do). You should make sure you’re using modal auxiliary verbs correctly in your speaking and writing. Can and may, for example, are not always interchangeable. Can indicates ability, while may indicates possibility. This might come up when you’re asking permission for something. You’re asking for the possibility of doing something, so you should use may instead of can. It’s important to identify modal auxiliary verbs and how they’re used while reading. This will help you improve your own usage of them! MODAL AUXILIARY VERBS LESSON PLAN WORKSHEETS The Modal Auxiliary Verbs lesson plan includes three worksheets: an activity worksheet, a practice worksheet, and a homework assignment. You can refer to the guide on the classroom procedure page to determine when to hand out each worksheet. SENTENCES ACTIVITY WORKSHEET Students will work with a partner to complete the activity worksheet. Each pair will cut out the sets of modal auxiliary verbs on the worksheet, fold them, and place them in a container. They will then each choose a verb. One partner will correctly use their word in a sentence, and the other partner will respond to that statement using their own word. Students may also work alone or in groups for the activity. FILL IN THE BLANKS PRACTICE WORKSHEET The practice worksheet asks students to complete three short exercises. For the first, they will fill in the blanks in sentences with shall, should, will, or would. For the second, they will fill in the blanks with ought to, can, may, or must. And for the third, they will fill in the blanks with could or might. MODAL AUXILIARY VERBS HOMEWORK ASSIGNMENT For the homework assignment, students will write sentences correctly using each of the given auxiliary verbs. They will also circle the best auxiliary verb for each sentence. Worksheet Answer Keys This lesson plan includes answer keys for the practice worksheet and the homework assignment. 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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History of the Geneva Convention The Geneva Convention, a cornerstone of international humanitarian law, was drafted in response to the horrors of war and the growing awareness of the need to preserve the rights and dignity of individuals. The idea of providing care for wounded troops gained traction in the middle of the 19th century, and from there the Convention grew. After witnessing the suffering of injured troops firsthand at the Battle of Solferino in 1859, Henry Dunant became an outspoken proponent of the creation of voluntary relief groups. The International Committee of the Red Cross (ICRC) was founded in 1863 thanks to his efforts. In 1864, the first Geneva Convention was signed, establishing standards for the care of injured soldiers. This was a monumental moment in the growth of humanitarian law on a global scale. Later Geneva Conventions were adopted in 1906, 1929, and 1949 to provide even more protections for civilians and prisoners of war during times of war. The Additional Protocols of 1977 supplemented the Geneva Conventions by addressing topics such as the protection of victims in internal armed conflicts. The concepts of humanism, neutrality, and impartiality have been emphasized in these accords to establish guidelines for the treatment of humans during times of war. The history of the Geneva Convention demonstrates humanity’s dedication to reducing casualties in times of war. Beyond the realm of law, it has an impact on the moral and ethical decisions made during times of crisis and war all over the world.

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Gender equality is one of the core principles of human rights. However, in many parts of the world, girls and women still face significant barriers to accessing education. Women are less likely to have access to education than men, and when they do attend school, they are less likely to have access to quality education. Girls in particular face discrimination and are often forced to drop out of school due to early marriage or pregnancy. Promoting gender equality and inclusivity in education is essential for creating a fairer and more just society. Gender equality in education is about ensuring that all students, regardless of gender, have equal access to quality education and are able to fulfill their potential. It is also about creating an inclusive environment where all students feel valued and supported. One of the key ways to promote gender equality and inclusivity in education is by addressing gender stereotypes. Stereotypes about what is appropriate for boys and girls often lead to a lack of interest in certain subjects. For example, girls are often discouraged from pursuing STEM fields, such as science and math, because they are perceived as being more suited to “feminine” subjects like literature and the arts. Similarly, boys may be discouraged from pursuing literature and the arts because they are perceived as “feminine” subjects. To address these stereotypes, educators should provide students with a variety of role models who challenge traditional gender roles. Teachers can also encourage students to explore subjects that they may not have considered before, regardless of gender. For example, teachers can encourage girls to participate in science experiments and boys to write creatively. Another important way to promote gender equality and inclusivity in education is by ensuring that students have equal access to resources. This includes textbooks, computers, and other learning materials. Girls are often disadvantaged in this area as they may not have the same access to resources as boys. This can make learning more difficult for girls, which in turn can lead to a lack of interest in education. To address this, schools can provide equal access to resources to all students. For example, schools can provide laptops or tablets to students in order to ensure that they have equal access to technology. Additionally, schools can provide libraries and other resources that are accessible to all students. Creating an inclusive environment is also essential for promoting gender equality. This means creating an environment where all students feel valued and supported, regardless of their gender. Teachers can promote inclusivity by creating a safe and welcoming classroom environment where students feel comfortable expressing themselves. This can include creating an environment where all students are encouraged to participate in classroom discussions and activities. In conclusion, promoting gender equality and inclusivity in education is essential for creating a fairer and more just society. This includes addressing gender stereotypes, providing equal access to resources, and creating an inclusive environment. By promoting these principles, educators can help to ensure that all students, regardless of gender, have equal access to quality education and are able to fulfill their potential.

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There have been large extinctions throughout Earth’s history. The most famous of these caused the end of the dinosaurs about 65 million years ago. At that time, about seventy percent of all the species on earth died out. Although dinosaurs had been in a period of decline before the extinction, it is thought that they could have recovered if something terrible had not prevented it. The most accepted theory about the cause of this extinction is the asteroid theory. It is believed that an asteroid about 10 kilometers in diameter hit the Earth. It is suggested that the asteroid destroyed everything within about 500 kilometers of where it landed. It would also have caused fires, increased volcanic activity, and sent huge clouds of dust, gases, and water vapor into the atmosphere. Because of this, there would have been months of darkness, cooler temperatures, and acid rain. There is a huge crater off the northwest tip of the Yucatan Peninsula in Mexico. The crater has been dated as 65 million years old and is believed to be evidence of a large asteroid impact.

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Bullying is repeated and deliberate aggressive behaviour intended to harm, intimidate, or dominate another person or group who is perceived as weaker or more vulnerable. In schools, it often involves a power imbalance, where the bully uses strength, social status, or influence to control or manipulate the other student. Bullying can take various forms, including physical, verbal, social, and cyberbullying. It can occur in various settings, such as schools, workplaces, online platforms, and social environments. Key characteristics of bullying include: Repetition: Bullying involves repeated instances of negative behaviour or actions over some time, rather than a one-time occurrence. Intention: The bully’s actions are purposefully meant to hurt, harm, or distress the target. Harm: Bullying causes emotional, psychological, or physical distress to the target. It can lead to feelings of fear, anxiety, humiliation, and isolation. Negative Impact: The target’s overall well-being is negatively affected by the bullying, leading to a decline in mental health, self-esteem, and social interactions. How to Cope With Bullying in School Coping with bullying on campus can be challenging, but there are several strategies you can employ to help navigate this difficult situation. Bullying can have serious emotional and psychological effects, so it’s important to prioritize your well-being. Here are some steps you can take: Stay Calm and Confident: It’s essential to maintain your composure when dealing with bullies. Keep your emotions in check and stand tall. Bullies often target those who appear vulnerable. Safety First: If the bullying involves physical harm or poses a threat to your safety, don’t hesitate to seek help from campus security or law enforcement. Your safety is paramount. Document Incidents: Keep a record of all instances of bullying. Note dates, times, locations, and descriptions of the incidents. This documentation can be valuable if you need to report the bullying to authorities. Talk to Someone: Reach out to a trusted friend, family member, teacher, counsellor, or any other supportive individual. Talking about your experience can provide emotional relief and help you gain perspective. Report to Authorities: If the bullying persists or escalates, report it to the appropriate campus authorities, such as a counsellor, teacher, or principal. They are trained to handle such situations and can intervene on your behalf. Practice Assertiveness: Stand up for yourself calmly and assertively without resorting to aggression. Use strong body language and confident verbal responses to discourage further bullying. Build a Support Network: Surround yourself with friends who uplift and support you. A strong support network can provide emotional strength and help you feel less isolated. Engage in Activities: Pursue your hobbies and interests outside of the bullying situation. Engaging in activities you enjoy can boost your self-esteem and provide a positive outlet for stress. Practice Self-Care: Take care of your physical and mental well-being. Engage in regular exercise, maintain a balanced diet, get sufficient sleep, and practice relaxation techniques like meditation or deep breathing. Seek Professional Help: If the bullying is severely affecting your mental health, consider reaching out to a mental health professional, such as a therapist or counsellor. They can provide guidance and coping strategies. Explore Conflict Resolution: If you feel comfortable, try discussing the issue with the bully in a controlled environment, with a mediator present if necessary. Sometimes, open communication can lead to understanding and resolution. Stay Online-Mindful: If cyberbullying is involved, limit your engagement with social media platforms where the bullying is taking place. Block or unfollow the individuals involved, and report abusive content. Know Your Rights: Familiarize yourself with your campus’s policies on bullying and harassment. You have the right to an education in a safe and respectful environment. Remember that coping with bullying takes time, and different strategies might work for different situations. It’s important to prioritize your well-being and take steps to protect yourself. If the bullying persists despite your efforts, don’t hesitate to seek external support and guidance. Credit: UNSW Newsroom – UNSW Syd What’s your impression about this story? Kindly like and share.

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Last week's story was a modern fable. Recall what we mean by a fable. If a fable is a story that has a moral lesson on how to behave and what to do what do you think the messages in this story, named "The Tree" will be? Write the class predictions up on the whiteboard wall. Look at the front cover. What do you think is going to happen in the fable? What are the two humans doing in front of the tree? What other characters are on the front cover? What might be their role in the fable? What clue is there on the front cover as to what might be going to happen in this story? Reading and Discussing Read the story together. Pause occasionally to discuss. Look closely at the expressions on the faces of the couple as they discover what is in their tree and when they understand what has happened to the nest. How many animals called the tree home? What did the couple do, to show us that they cared for the environment? What did they do to show us that humans and the environment can co-exist? What message does the author give us about how we should treat the environment? Discuss the simple text and count how many sentences are in the whole story. Why is the text so simple? What does this tell us about the beliefs of the author? How effective is this text in getting a very strong message across? Do you need to have a lot of words to get a message across? Look back at the whiteboard to your predictions about the moral lessons from this fable. Which ones were correct? Now that you have finished reading, what important messages could you add?

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The Historical Context The Berlin Wall, erected in 1961, stood as a physical and symbolic division between East and West Berlin during the Cold War. Its construction was initiated by the German Democratic Republic (GDR) to prevent mass emigration from East to West. This formidable barrier spanned 96 miles, effectively cutting off families, friends, and communities. Life in East Berlin Living in East Berlin under the communist regime presented its own set of challenges. The GDR imposed strict control on its citizens, impacting their daily lives in various aspects. One of the key aspects was the command economy, where the government controlled the means of production. This resulted in limited consumer choices and a lack of economic prosperity compared to West Berlin. The state-controlled media also played a significant role, shaping public opinion and disseminating propaganda. Citizens were subject to heavy surveillance, limiting their freedom of expression and creativity. Moreover, those living in East Berlin faced restricted travel and limited access to foreign culture and ideas. The government imposed ideological conformity and restricted contact with the outside world, isolating individuals from the global community. Life in West Berlin On the other side of the wall, West Berlin experienced a contrasting reality. As part of West Germany, it benefited from a capitalist economy that thrived on private enterprise and entrepreneurship. West Berlin offered a higher standard of living with access to a wide range of consumer goods and services. The city became a vibrant cultural hub, attracting artists, musicians, and intellectuals from around the world. Individual freedoms were championed in West Berlin, with freedom of speech, press, and assembly being protected by the constitution. This fostered an environment where creativity and innovation flourished. Additionally, the people of West Berlin enjoyed freedom of movement, enabling them to travel and explore the wider world without encountering the same restrictions imposed in the East. The Human Cost While West Berlin appeared more prosperous and offered greater personal freedoms, it’s essential to acknowledge the significant human cost associated with the division. The construction of the Berlin Wall resulted in the separation of families, friends, and loved ones. Many East Berliners risked their lives attempting to cross into West Berlin, with some paying the ultimate price. The wall served as a physical manifestation of the Cold War rivalry, instilling fear, despair, and psychological distress among the people of Berlin. It created a sense of distrust and animosity, further deepening the divide between the two sides. The Catalyst for Change Over the years, the Berlin Wall became a symbol of oppression and an affront to human rights. The restrictions imposed on East Berliners eventually led to growing discontent and a yearning for change. Public protests and demonstrations in East Berlin and other parts of the GDR played a pivotal role in the fall of the Berlin Wall. In November 1989, the wall crumbled as East and West Berliners came together to celebrate their newfound freedom. The Legacy and Reunification The fall of the Berlin Wall marked a significant turning point in history, not only for Berlin but for the world. It signaled the end of the Cold War and the collapse of communism in Eastern Europe. The reunification of East and West Germany in October 1990 brought immense challenges but also opportunities. The process of reunification involved merging two distinct political, economic, and social systems. Today, Berlin stands as a vibrant, united city, buzzing with creativity, culture, and historical significance. While the scars of the past are still visible, the city has embraced its history and transformed into a symbol of resilience and hope. The Importance of Remembering It is crucial to remember the division created by the Berlin Wall, the suffering endured by its citizens, and the lessons it taught us. The wall serves as a stark reminder of the impact political ideologies can have on the lives of ordinary people. By understanding the complexities and consequences of this divisive barrier, we can strive to build bridges instead of walls, fostering unity, understanding, and a commitment to human rights. As we commemorate those affected by the Berlin Wall, may we never forget the power of freedom, unity, and the resilience of the human spirit. Table of Contents

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Lesson Plans and Worksheets Browse by Subject Estimation Teacher Resources Find teacher approved Estimation educational resource ideas and activities Youngsters count, classify, and estimate quantities using buttons after a read aloud of The Button Box by Margarette S. Reid. They discuss the difference between guessing and estimating. Based on an experiment, they predict the number of buttons a pair of students can hold. Each creates an individual button book to communicate results. Then the class constructs and analyzes a line plot. An integrated activity that adapts easily to a wide range of mastery levels. Review and use standard units of measure with your math class. They move from station to station estimating and measuring length, volume, weight, and area. At each station they estimate and measure, and then compute the difference between the two. They practice linear measurement estimation skills by throwing cotton balls and rolling toy cars. In a cross-curricular measurement and literacy activity, your class will identify and compare cooking measurement instruments. They read a recipe and sequence a set of similar instructions in which the steps have been mixed up. Additionally, they practice measurement conversion and ratio while solving a word problem that asks the students to use only a tablespoon to estimate their measurements while following a cookie recipe. Upper graders explore the part-whole relationships in fractions. Using fraction strips, they model the addition of fractions and discover equivalent fractions. In pairs, they estimate the sum of fractions, and then record the proper sum, writing sentences to justify their answer. To reinforce the addition of fractions and equivalent fractions, they participate in an "Each-One-Teach-One" activity. Additional activities are provided. Test a variety of beginner math skills with this comprehensive assessment, which includes fifteen questions prompting addition, subtraction, estimation, and place value practice. An advantage to this assessment is the visual appeal; although there are no images, the questions are arranged with visual variety, and include space for learners to show work. Some are multiple choice, while others are fill-in-the-blank or even require using a number line. Fourth graders complete fraction estimation and comparisons by studying physical and visual models of fractions. They work in partners to sort index cards into titled fraction groups. They review improper fractions, mixed numbers, and proper fractions and write what they learned about estimating fractions to one-half and whole numbers in their journals.

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Order of magnitude is the magnitude of any amount, in which there is a fixed ratio in which the particular class is different to the preceding, or the succeeding class by a fixed value. This fixed value is in the form of a ratio, and the most common ratio which is used all around is the power of ten. Hence, in the most common way, we can conclude that the Order of Magnitude of a value, at a particular class, is ten times higher than its preceding class, or ten times less than its succeeding class. One most common example is the Richter scale. The Richter scale is used to measure the earthquakes, and when we commonly say that “an earthquake measuring 7 on the Richter scale has occurred”, we basically want to say that the earthquake, which has occurred is 10^7 times stronger than the earthquake on the Richter scale 1`. Like a common parameter, the Richter scale also uses a parameter of 10, for its order of magnitude. Common Uses of Order of Magnitude: An order of magnitude is used to compare the difference on an approximate basis, but the actual difference between the magnitudes is very large. Like we just discussed in the example of earthquake, the earthquake at a scale of 3, is a hundred times more powerful than the earthquake on Richter scale one. The order of magnitude is obtained by the truncation of the value, to find the integer part of the logarithm. So, the order of magnitude becomes the power of 10 contained in the number. This value is obtained by finding the logarithm of that particular number to the base ten, and if the figure calculated is not integer, then the truncation of the total figure is done, and the integer part of the figure is the Order of Magnitude of that number. Let us consider an example. If the number 4000000 is given to us, then by finding the logarithm of the number, gives us a value of around 6.602. So, the common process as stated, the truncation of the value gives us six. Hence, the order of magnitude of the number 4,000,000 comes out to be six. Order of Magnitude Estimate: An Order of Magnitude estimate is said to be done of those values, which are too high, to estimate their Order of Magnitude. So, an estimate of the order of magnitude is to be conducted. Let us consider an example for this as well. How, to consider an order of magnitude for human population, which lies between three and thirty billion. It is ten billion. Extremely Large Numbers: For very large numbers, double or super logarithm, can be conducted. The first logarithm gives a very large digit, and the second logarithm gives the category of very large numbers. Extremely Small Numbers: For very small numbers, neither of the methods cannot be suited. However, a reciprocal method can be considered for it.

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To figure out the formula of an ionic compound you need to 1) identify the ions, then 2) create a neutral compound from those ions. Example. To write the formula for sodium sulfide requires the following steps: 1. Recognize that sodium ions are Na+ and sulfide ions are S2-. 2. Combine these two ions so that the total charge is zero. In this case, it take two 1+ charges per one 2- charge. Thus the formula for sodium sulfide is Na2S. This handout focuses on the second step. The main conceptual issue is that ionic compounds are neutral. Ions have charge, such as the +1 charge on a sodium ion, Na+. Ionic compounds, however, are neutral. If you know the ions, you can figure out the formula of an ionic compound by calculating how many of each ion you need to achieve neutrality -- to have the same number of positive charges and negative charges. People use various mental tricks to figure out how many ions are needed to reach neutrality. After a little practice, you will do many of these “by inspection.” One trick is to “cross multiply.” (This is similar to finding the least common denominator when adding fractions.) Example. Write the ionic compound between Mg2+ and Cl- (magnesium and chloride ions). The charges are 2+ and 1-. Take 1 of the 2+, 2 of the 1-. The result: MgCl2 (magnesium chloride), which has 2 + charges and 2 - charges. Caution. Check that your formula is the simplest formula possible (i.e., the empirical formula). This is especially important if you use the cross multiply method. Example. Write the ionic compound between Ca2+ and O2- (calcium and oxide ions). The charges are 2+ and 2-. Using the cross multiply method, take 2 of the 2+, 2 of the 2-. The result: Ca2O2. This is neutral (4 each + and - charges), but it is not the simplest -- or proper -- formula. Simplify to CaO (calcium oxide). In the problems that follow (see back of page), you are given two ions, and asked to write the formula of the ionic compound that could form between them. Since you are given the ions, including the correct ion charges, all you need to do is to achieve neutrality. You can do these sections in any order; do problems that help you. If you have trouble at first, check yourself as you go. Seek help if necessary. A. This section uses real monatomic ions. Most of these are common ions that you should be able to figure out from the periodic table; however, you are given the ions, including the charge. All you need to do is to achieve neutrality. 1. Na+ and S2- 2. Na+ and N3- 3. Al3+ and Cl- 4. Pb4+ and Cl- 5. Pb4+ and O2- 6. Ca2+ and S2- 7. Al3+ and Br- 8. Ca2+ and N3- 9. Ca2+ and Br- 10. Al3+ and S2- 11. Al3+ and N3- 12. Mg2+ and P3- B. This section uses real (and common) ions, including both monatomic and polyatomic ions. Note that all the polyatomic ions shown here are ones you should know. 13. Na+ and SO42- 14. Na+ and PO43- 15. K+ and PO43- 16. NH4+ and Br- 17. Mg2+ and SO42- 18. Al3+ and NO3- 19. Ca2+ and CO32- 20. Ca2+ and PO43- 21. Ca2+ and NO3- 22. NH4+ and S2- 23. Pb2+ and OH- 24. NH4+ and SO42-

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Algebra Worksheets Algebra Worksheets Algebra Worksheets, which are online available for free must be used by the students to get the exposure to the algebra. On working with Algebra Worksheets, you will avail confidence about the concepts of Algebra. Algebra is basically the combinations of basic relations expressed in form of statements. It comprise of the alphabets used to express the variables and the operators. Any statement of algebra can be formed by joining the terms combined by the help of the operators. It is also termed as an algebraic expression. Algebra can help in solving the expressions and yielding the results. Any algebraic equation is formed by equating the left hand side and the right hand side expression of the equation. In order to get the result of the variable in the equation, we simply have to take care of the following rules: 1. Always try to bring all variables on one side of the equation and the constants to the other side of the equation. Know More About Product Rule Math.Tutorvista.com Page No. :- 1/4 2. We must remember that when the Variables or the constants are moved from one side of the equation to another side , first we must take care of addition and subtraction relation and then followed by multiplication and division relations in the expression. 3. When any expression with positive sign is taken to another side of the equation, then the expression becomes negative and if the expression is with negative sign and it is taken to another side of the equation, then the sign becomes positive. 4. If any variable or constant with multiplication relation is taken to another side of the equation, it becomes divide and if the relation is division, it changes into the relation of multiplication. It order to learn how to solve the algebraic equation, we must start with an example: Let 2x + 7 = x +20 Here we will try to bring all the terms with x on one side of the equation and the terms without x on another side of the equation. These terms must be moved with the terms and conditions learned earlier. So we get: 2x – x = 20 – 7 Or x = 13 This value of x is correct or not can be verified by putting the value of x expression and then check if LHS = RHS or not. in the given Solve 5y + 300 = 2y – 150 Learn More :- Simple Interest Calculator Page No. :- 2/4 We will bring all the terms with Y on one side of the equation and get; 5Y – 2Y = -150 -300 Or 3y = -450 Now we need to remove 3 from Y, in order to get the value of Y. So we will take 3 on another side of the equation with division sign and the equation becomes: Y = -450 / 3 Or y = -150 Now we can verify if the result we get as the value of y is correct or not. For this we put the value of Y in the given equation and check if the value satisfies the equation or not. Page No. :- 4/4 Thank You For Watching

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Start a 10-Day Free Trial to Unlock the Full Review Why Lesson Planet? Find quality lesson planning resources, fast! Share & remix collections to collaborate. Organize your curriculum with collections. Easy! Have time to be more creative & energetic with your students! Solving Systems Using Linear Combination Students explore the concept of solving systems of equations using linear combination. In this systems of equation lesson, students solve systems of equations using linear combination. 3 Views 12 Downloads Using Linear Equations to Define Geometric Solids Visualizing three dimensions from a two-dimensional drawing is challenging. Give your class a reference by focusing on the revolution of the cross-section. In this Common Core math lesson plan, pupils create a three-dimensional solid... 9th - 10th Math CCSS: Designed New Review Introduction to Simultaneous Equations Create an understanding of solving problems that require more than one equation. The lesson introduces the concept of systems of linear equations by using a familiar situation of constant rate problems. Pupils compare the graphs of... 8th Math CCSS: Designed Solving Systems of Linear Equations Graphing Do you need to graph lines to see the point? A thorough lesson plan provides comprehensive instruction focused on solving systems of equations by graphing. Resources include guided practice worksheet, skill practice worksheet, and an... 8th - 10th Math CCSS: Adaptable Simultaneous Linear Equations Solve simultaneous linear equations, otherwise known as systems of linear equations. Pupils practice solving systems of linear equations by graphing, substitution, and elimination. The workbook provides a class activity and homework for... 7th - 10th Math CCSS: Designed Solving Systems of Linear Inequalities One thing that puzzles a lot of young algebrists is the factors in a word problem that are taken as "understood". This presentation on solving systems of linear inequalities does a great job walking the learner through how to tease those... 9th - 10th Math CCSS: Adaptable Solving Systems of Linear Equations Solving systems of equations underpins much of advanced algebra, especially linear algebra. Developing an intuition for the kinds and descriptions of solutions is key for success in those later courses. This intuition is exactly what... 8th - 9th Math CCSS: Adaptable Topic 4: Solving Systems of Linear Equations Linear equations, coordinate planes, and systems of equations are covered in this extremely well-organized lesson. Composed of a series of mini-lessons, the instruction aims at explaining a different facet of solving systems of linear... 8th - 11th Math CCSS: Adaptable Systems of Equations: What Method Do You Prefer? Students explore the concept of solving systems of equations. In this solving systems of equations lesson, students watch YouTube videos about how to solve systems by graphing and by elimination. Students use an interactive website to... 8th - 12th Math CCSS: Designed Applying Systems of Equations - Finding Break-Even Points Explore the concept of solving systems of equations with this project by finding the break-even points using linear equations. Learners need to interpret their graphs in terms of their real-world meaning and make recommendations based on... 8th - 9th Math CCSS: Adaptable

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Start a 10-Day Free Trial to Unlock the Full Review Why Lesson Planet? Find quality lesson planning resources, fast! Share & remix collections to collaborate. Organize your curriculum with collections. Easy! Have time to be more creative & energetic with your students! Creating and Understanding Circles and Their Parts Sixth graders explore and construct circles, using such tools as compasses and rulers. They also develop definitions for identifying the center, radius, diameter, chord, and circumference. 4 Views 14 Downloads Relationships Between Quantities and Reasoning with Equations and Their Graphs Graphing all kinds of situations in one and two variables is the focus of this detailed unit of daily lessons, teaching notes, and assessments. Learners start with piece-wise functions and work their way through setting up and solving... 6th - 10th Math CCSS: Designed The Circumference of a Circle and the Area of the Region it Encloses Bring your math class around with this task. Learners simply identify parts of a given circle, compute its radius, and estimate the circumference and area. It is a strong scaffolding exercise in preparation for applying the formulas for... 6th - 8th Math CCSS: Designed Teaching Masters and Study Link Masters Help young mathematicians shape their understanding of geometry with this series of worksheets and activities. Starting with an introduction to line segments, lines, and rays, the first unit in this math series continues on to explore... 4th - 6th Math CCSS: Adaptable Get on your Mark, Get Set, Go! Collect, Interpret, and Represent Data Using a Bar Graph and a Circle Graph Start an engaging data analysis study with a review of charts and graphs using the linked interactive presentation, which is both hilarious and comprehensive. There are 27 statistics-related vocabulary terms you can use in a word sort.... 4th - 7th Math CCSS: Designed

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ExplanationThe structural categories we can assign an element or group of elements to, such as word classes, phrases, and clauses. Form is distinct from the function that an element or group plays within a larger structure. For example, a group of words with the form of a noun phrase can have different functions in the clause, such as Subject or Direct Object. The term 'form' is also used to refer to the 'shape' or morphology of words. A quick activity looking at how some words can be both nouns and verbs This is a simple starter activity that will help your students see how some words can function as both nouns and verbs. The activity is designed to be carried out in pairs around the class. One student be the noun and the other will be the verb. Each will need the same word list (which you can download and print below) or you can just use the word list on the screen. A useful distinction in grammar is that of form and function. Grammatical form is concerned with the description of linguistic units in terms of what they are, and grammatical function is concerned with the description of what these linguistic units do. Note that we use capital letters at the beginning of function labels. Verbs have traditionally been described as ‘doing words’ or ‘action words’. This works well for some verbs, like sprint, chatter, eat. Here are some sentence examples with verbs which describe actions: Englicious contains many resources for English language in schools, but the vast majority of them require you to register and log in first. For more information, see What is Englicious?

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This flow chart can be used in many ways to strengthen student understanding of matter and its three states.- Print as a large anchor poster for quick student reference- Print small to fit in student science notebooks- Print one of the three flow charts that have some or all parts missing to use as scaffolded notes or as an assessment. States of Matter: Solids, Liquids, and Gases Study Guide Outline - Characteristics of Matter - King Virtue's Classroom Starting your unit on Matter? Help your students get off to a great start with this simple study guide outline. This is a great tool that can be used to inform your parents about what their children will be learning about the three states of matter (solid, liquid, and gas) and the characteristics of each phase. This 27-page science mini-book was created to help teach the Next Generation Science Standards for 2nd grade in structure and properties of matter. It covers the following principles: what is matter, different states of matter, how matter can change, reversing states of matter, and observable properties of matter. This video/animation defines matter, mass, and volume using water as an example. The size, electrical charge and location of the subatomic particles of matter are described. Different types of atoms are called elements and organized in the periodic table. What happens to the properties of atoms when they exist alone or together?.

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During the reign of the Catholic monarchs (15th century), the accumulation of huge territories because of this marriage and future conquests, made the Spanish Empire became difficult to control directly. For that, the kings created the form of Viceroyalty that could be defined as a regional division within the Empire. That portion of land was led by the viceroy, the official most important and direct in the hierarchy under the King. Being land of large size, typically all functions could be controlled by the viceroy, whether political, economic, social and legal functions. In the case of America, territories were yes or Yes organize this form since, due to the distance of the same with Spain, the presence of the Spanish kings of the day was impossible. Thus, the Spanish Crown organized regions conquered on viceroys who were, in general, very widespread and abundant (therefore, difficult to control even though officials were in them). The most important viceroyalties of the colonial period were those of new Spain (present territories of Mexico and Central America), the Peru and Nueva Granada (current territory of Venezuela). The case of South America was a case apart since the territories would not exploited and organized as Viceroyalty until 1776, moment in which was established the Viceroyalty of the Río de la Plata. This Viceroyalty would be that less time would last since nearly forty years later would start the wars of independence between the Creole and Spanish revolutionaries who would make that the power of the Spanish Crown ended disappearing from these regions of the planet. Article contributed by the team of collaborators.

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How Hot or Cold Does It REallu Feel Students explore 3-D graphing with the TI-92 or TI-89. In this secondary mathematics lesson plan, students create 3-D graphs as they explore the formulas for calculating the heat index and wind chill . 3 Views 2 Downloads Money Matters: Why It Pays to Be Financially Responsible What does it mean to be financially responsible? Pupils begin to develop the building blocks of strong financial decision making by reviewing how their past purchases are examples of cost comparing, cost-benefit analysis, and budgeting. 9th - 12th Math CCSS: Adaptable New Review Box-and-Whisker Plots The teacher demonstrates how to use a graphing calculator to create box-and-whisker plots and identify critical points. Small groups then create their own plots and analyze them and finish by comparing different sets of data using box... 10th - 12th Math CCSS: Adaptable The Power of Exponential Growth How do you make a penny grow to $5,000 in just 15 days? Use the examples in this instructional activity to explore the concept of exponential growth and its comparison to linear models. Pupils come to understand that exponential growth... 9th - 10th Math CCSS: Designed Module 3: Arithmetic and Geometric Sequences Natural human interest in patterns and algebraic study of function notation are linked in this introductory unit on the properties of sequences. Once presented with a pattern or situation, the class works through how to justify... 8th - 10th Math CCSS: Adaptable Representing Inequalities Graphically A new, improved version of the game Battleship? Learners graph linear inequalities on the coordinate plane, then participate in a game where they have to guess coordinate points based on the solution to a system of linear inequalities in... 9th - 12th Math CCSS: Designed

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A lithosphere is the rigid, outermost shell of a terrestrial-type planet or natural satellite that is ... The Lithosphere-Asthenosphere boundary is defined by a difference in response to stress: the lithosphere remains .... "attached" to the continental plate above, similar to the extent of the "tectosphere" proposed by Jordan in 1988. The asthenosphere is the highly viscous, mechanically weak and ductilely deforming region of the upper mantle of the Earth. It lies below the lithosphere, at depths between approximately 80 and 200 km (50 and 120 miles) below the surface. The Lithosphere-Asthenosphere boundary is usually referred to as LAB. .... In other projects. The difference between asthenosphere and lithosphere is how the materials in these layers can flow. Rocks in the lithosphere are "rigid", meaning that they can ... Make research projects and school reports about asthenosphere easy with ... In addition to loss of pressure on the asthenosphere, another factor that can bring ... they approach Earth's surface and eventually become part of the lithosphere itself . ... partially molten) rock material chemically similar to the overlying lithosphere. Apr 25, 2017 ... The lithosphere and asthenosphere form the upper two layers of the earth. ... These rocks behave elastically, although they are brittle and can break, fracture ... and pressure maintains a consistency similar to that of warm tar. Sep 11, 2013 ... Lithosphere; Asthenosphere; Upper mesosphere; Lower mesosphere ... of the different set of layers individually before exploring how they overlap. ..... the earth an overall composition similar to the composition of other objects ... Aug 31, 2016 ... Lithosphere - about 100 km thick (up to 200 km thick beneath ... Asthenosphere - about 250 km thick - solid rock, but soft and flows easily (ductile). ... atoms in a glass are arranged randomly similar to the arrangement in a liquid). ... If the crystallization takes place on the surface of the Earth they are called ... It is easy to assume that they were not formed for the sole purpose of downhill skiing. ... The earth contains three layers of different composition. ... It is rock strength that differentiates the lithosphere from the asthenosphere. .... The back- arc region is similar to a major spreading axis, but there are some differences between ... Aug 11, 2015 ... Different types of rocks distinguish lithospheric crust and mantle. ... The temperature and pressure of the asthenosphere are so high that rocks .... Instruments placed around the world measure these waves as they arrive at different points on the Earth's surface after an earthquake. ... to match or be similar to. The asthenosphere is hotter than the lithosphere because it is nearer to the core. ... Similar to the outer core, the inner core is mainly made up of iron and nickel ...

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Department of Mathematics Education be asked to set up a spreadsheet, enter data into it, and use the spreadsheet’s functions to analyze the data. They also will see how the spreadsheet can be used to make a graph of the data. Then they will compare the spreadsheets. To get the students’ attention, explain that each cell in a spreadsheet has an address, or name. Provide students with a blank table that has 3 columns and 3 rows. Have them label the columns with the letters A, B, and C and label the rows 1, 2, and 3. Have them work in pairs to devise a way to use the letters and numbers to name each cell in the table. Ask each pair to share their ideas with the Have the students work individually to answer all question on the lab sheet. Once the activity has been completed, students can compare answers to see if there are any discrepancies. To bring the class back together, have them suggest real-world situations in which spreadsheet tables might be useful. Have each student choose one situation, research appropriate data, and create a spreadsheet. This problem has many aspects you can go into, data entry, functions, and use of technology. It also has many entry and exit points. to Matt’s Homepage

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In this grammar worksheet, 3rd graders circle the correct homophone to complete 10 sentences. They choose between two homophones in each example. 3 Views 2 Downloads All About Homophones Put the fun back in reading fundamentals with an interactive set of lessons about homophones. Learners of all ages explore the relationships between words that sound the same but have different meanings, and complete a variety of fun and... 1st - 8th English Language Arts CCSS: Adaptable Homophones and Homonyms Whether or not your class has heard of homonyms, they'll herd together to complete a language worksheet! With examples of both homophones and homonyms, the worksheet prompts learners to come up with additional pairs of words that sound... 1st - 3rd English Language Arts CCSS: Adaptable Never mix up principle and principal again with a helpful homophones worksheet. Featuring ten pairs of words that have the same sounds but different meanings, the worksheet prompts your class to fill in the blanks with the appropriate... 2nd - 4th English Language Arts CCSS: Adaptable Practice Book O Whether you need resources for reading comprehension, literary analysis, phonics, vocabulary, or text features, an extensive packet of worksheets is sure to fit your needs. Based on a fifth-grade curriculum but applicable to any level of... 3rd - 6th English Language Arts CCSS: Adaptable Big Grammar Book With this comprehensive language arts resource in your arsenal, you'll never have to look for another grammar worksheet! Whether you're teaching kindergartners how to write the upper- and lower-case letters of the alphabet, or helping... K - 8th English Language Arts CCSS: Adaptable

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(text reference: Section 3.1) ▯V. Olds 2010 Unit 7 91 7 Matrix Operations At the beginning of Unit 6, we defined the mathematical construct called a matrix. Next we learn more about matrices, especially how to do matrix arithmetic. First, we should review the definition of a matrix. And define one more term, that we didn’t need in what we have done so far. Definition: A matrix is a rectangular array of numbers: a11 a12 a13 ▯▯▯ a1n a21 a22 a23 ▯▯▯ a2n . . . . . . . . am1 am2 am3 ▯▯▯ amn The horizontal lines of numbers are called rows and the vertical lines of numbers are called columns. The number, aij in row i and column j is called the (i,j)-entry of the matrix. A matrix with m rows and n columns is called an m × n matrix (pronounced “m by n”). The numbers m and n are called the dimensions of the matrix. When one of the dimensions of a matrix is 1, so that the matrix has only one row or one column, the matrix is very similar to a vector. Because of that, we sometimes use the word vector in describ- ing the matrix. But we need be clear about which dimension is 1, so we qualify the term vector. This also helps to remind us that we’re really talking about a matrix, rather than an actual vector. Definition: For any value n > 1, a 1 × n matrix can be referred to as a row vector. Similarly, for any value m > 1, an m×1 matrix can be referred to as a column vector. Example 7.1. Describe each of the following matrices, and identify both the (1,2)-entry and the (2,1)-entry, if the matrix has one. ▯ ▯ 3 4 0 ▯ ▯ ▯ ▯ (a) 1 2 3 (b) 5 6 (c) 1 (d) −3 0 3 2 (e) −32 4 5 5 7 7 8 2 (a) Since the matrix 1 2 3 has 2 rows and 3 columns, it is a 2 × 3 matrix. The (1,2)-entry 4 5 5 of this matrix is 2 (i.e. the number in row 1, column 2), and the (2,1)-entry is 4 (i.e. the number in row 2, column 1). (Notice that both in stating the dimensions of the matrix and in referring to a particular entry, the first number always refers to row(s).) (b) The matrix 5 6 has 5 rows and 2 columns, so it is a 5 × 2 matrix. The (1,2)-entry is 2 and the (2,1)-entry is 3. 92 Unit 7 (c) We have the matrix 1 , which has 3 rows and only 1 column, so this is a 3×1 column vector. Since it doesn’t have any column 2, there is no (1,2)-entry. The (2,1)-entry is 1. (d) This matrix, −3 0 2 , has only 1 row, with 4 columns, so it is a 1×4 row vector. The (1,2)-entry is 0, and of course there is no (2,1)-entry. (e) Is that a matrix? Just −32 ? Sure it is. We can tell by the square brackets around it (as well as by the fact that the question said that each of the question parts involved a matrix). This matrix has only 1 row and 1 column. It is a 1 × 1 matrix, and therefore has neither a (1,2)-entry nor a (2,1)-entry. Its only entry is the (1,1)-entry, which is −32. Note: According to our definitions of row vector and column vector, the “other” dimension must be bigger than 1, so a 1 × 1 matrix is not considered to be either of these things. We just call it a 1 × 1 matrix (which helps us to re- member that it is a matrix, rather than just a scalar which happens to be written in square brackets.) There is some more terminology and notation for matrices that we should talk about. In vectors, we talk about corresponding components, meaning the numbers in the same position in 2 vectors in the same space. Similarly, when we’re talking about two matrices which have the same dimensions, we use the term corresponding entries to refer to the numbers in the same positions in the 2 matrices. So for instance if we have two m × n matrices, i.e. with the same values of m and of n for each, the (1,1)-entries of the 2 matrices are corresponding entries. And the (3,2)-entries of the matrices, if there are any, are also corresponding entries. In general, the (i,j)-entry of one ma- trix and the (i,j)-entry of the other matrix, for the same values of i and j, are corresponding entries. Matrices are named with capital letters. And when a matrix is named with a particular capital letter, we often use the lower case version of the same letter, subscripted with row and column indices, to denote entries in the matrix. For instance, if we have a matrix called A, we can ijtoa denote the (i,j)-entry of A. And then sometimes we want to define a matrix as the matrix A whose (i,j)-entry is calledij . We do this by saying “Let A = [aij”, or “Consider the matrix A = [aij”. So [a ] simply denotes the matrix containing entries which are referred to as a . For instance, we could say “Consider the 2 × 3 matrix A = [a ]ijith a ij= i − j”, which defines A to be the 2 × 3 matrix in which each entry is its row number minus its column number. So we would have ▯ 0 −1 −2 ▯ 1 0 −1 Here is some more terminology that we use: • Any matrix in which every entry is zero is called a zero matrix. So for any positive integers m and n, there is an m × n zero matrix. Notice: This is similar to the idea of the zero vector in ℜ . • For any n > 1, any n × n matrix is called a square matrix of order n. That is, a square matrix is just a matrix which has the same number of rows and columns. And the order of the matrix is the number of rows (or the number of • In a square matrix of order n, the entries aii for i = 1,...,n are called the main diagonal of the matrix. That is, the main diagonal of a square matrix runs diagonally, from the top left corner to the bottom right corner of the matrix. Unit 7 93 • Any matrix in which the only non-zero entries appear on the main diagonal is called a diagonal matrix. So in a diagonal matrix, all the entrieijfor i ▯= j are 0. Of course, there may also be some zeroes along the main diagonal. • The identity matrix of order n is the n×n diagonal matrix in which a ii1 for all i = 1,...,n. The identity matrix of order n is often denoted I , or just I. That is, an identity matrix is a square matrix which has 1’s all along the main diagonal, and 0’s everywhere else. Consider the matrices shown here: ▯ ▯ ▯ ▯ ▯ ▯ 0 0 1 2 0 0 0 A = B = C = 0 0 3 4 0 0 0 1 0 0 0 1 0 0 0 1 0 0 D = 0 2 0 I4= 0 0 1 0 0 0 −5 0 0 0 1 Here, A is the 2×2 zero matrix. It is also a square matrix of order 2. And since it is a square matrix, and all off-diagonal entries are 0, we could also say that it is a diagonal matrix. (Any square zero matrix can be said to be a diagonal matrix. But diagonal matrices usually do have some non-zero entries.) B is another square matrix of order 2. And C is another zero matrix — the 2 × 3 zero matrix. Matrix D is a square matrix of order 3, and since all the non-zero entries are along the main diagonal, with zeroes everywhere else, it is a diagonal matrix.4And I , of course, is the identity matrix of order 4. Which means it’s also a square matrix, and a diagonal matrix. (Notice: We’ve seen identity matrices before. A square matrix in RREF which doesn’t have any rows of only zeroes is always an identity matrix.) Some matrix concepts, definitions, and/or arithmetic operations are just like the corresponding concepts, definitions and/or arithmetic operations for vectors in ℜ . We’ve already seen some, like the zero matrix. Next we learn some more. • Matrix Equality: Two matrices are said to be equal if and only if they have the same dimensions, and their corresponding entries are equal. That is, A = B if and only if A and B are both m × n matrices (for the same m and n) and it is true thatij= bijfor all values of i and j. • Matrix Addition: If A and B have the same dimensions, then the sum of matrices A and B is obtained by summing the corresponding entries. So if A and B are both m×n matrices, the matrix C = A+B has c ij= a ij ij for all i and j. Notice that if A and B do not have the same dimensions, then A + B is not defined. We can only add matrices which have the same dimensions. • Scalar Multiplication: For any matrix A and any scalar c, the scalar multiple cA is obtained by multiplying every element of A by c. So the matrix B = cA has bij= c(aij for all i and j. • Negation: For any matrix A, the negative of A, denoted −A, is the matrix (−1)A. That is, each entry of −A is the negative of the corresponding entry of A, so if B = −A, then bij= −a ijfor all i and j. 94 Unit 7 • Matrix Subtraction: For any matrices A and B which have the same dimensions, the matrix difference A − B is defined to be the sum of A and −B. That is, if C = A − B, then C = A + (−B), so = a − b for all i and j. ij ij ij Notice that each of these works in exactly the same way as the analogous operation for vectors. Vectors can only be equal, or be added or subtracted, if they’re from the same space. For matrices, they must have the same dimensions. That is, in both cases, they must have the same number of entries (components), in the same configuration. And the scalar multiplication operation multiplies every element by the scalar, both for vectors and for matrices. Likewise, juv = (−1)v, we have −A = (−1)A for any matrix A. Example 7.2. State whether matrices A and B are equal. ▯ ▯ ▯ ▯ (a) A = 1 −2 3 B = 1 −2 3 4 0 6 4 0 6 ▯ ▯ ▯ ▯ (b) A = 1 0 3 B = 1 0 3 5 1 −2 5 1 2 1 2 3 1 4 (c) A = B = 2 5 4 5 6 3 6 ▯ ▯ 1 0 (d) A = 1 0 B = 0 1 (a) A = 1 −2 3 = B 4 0 6 Since A and B are both 2 × 3 matrices andij= bijfor each pair (i,j), they are equal matrices. ▯ 1 0 3 ▯ ▯ 1 0 3 ▯ (b) A = ▯= B = 5 1 −2 5 1 2 Although A and B are both 2 × 3 matrices, with many of their entries identical, there is a combi- nation ij for whichij▯= bij(i.e. 23= −2 whereas b 23= 2). Therefore, A and B are not equal 1 2 3 1 4 (c) A = ▯= B = 2 5 4 5 6 3 6 Here, A has dimension 2 × 3, whereas B has dimension 3 × 2, so they cannot be equal matrices, no matter how similar their entries may be. 1 0 1 0 (d) A = ▯= B = 0 1 0 1 0 0 Again, A and B do not have the same dimension (A is 2×2 while B is 3×2), so they are not equal. Unit 7 95 Before we look at more examples, there is one more matrix operation we should define. This one is not like any operation on vectors, because it involves changing the dimensions of the matrix, by interchanging the rows and columns, which has no counterpart in the context of vectors, since a vector has only one dimension. Effectively, we turn the matrix sideways, so that the rows become columns and the columns become rows. We refer to this as transposing, i.e. finding the transpose of, the matrix. Definition: For any m × n matrix A, the transpose of A, denoted A , is the n × m matrix whose (i,j)-entry is the (j,i)-entry of A. That is, if B = A , = an bfor all values of i and j. 1 2 3 For instance, to find the transpose of A = , the entries in the first row of A become 4 5 6 the entries in the first column of and the entries of the second row of A become the entries of the second column of A . Or, looked at the other way, the first column of A is the first row of A , the second column of A is the second row of and the third column of A is the third row of A . It doesn’t matter whether we think of switching rows to columns or switching columns to rows — the effect is the same. In terms of entries, iijB = [b ] where B = A , since A is a 2×3 matrix then B is a 3×2 matrix, with11 = a11 b12= a21 b21= a 12b22 = a22 b31= a13 and 32 = a23 We get ▯ 1 2 3 ▯T 1 4 A T = = 2 5 4 5 6 2 3 ▯ ▯ 1 a b Example 7.3. If A = −1 4 and B = c 2 −1 , are there any values of a, b and c for which A = 2B ? We see that A is a 3 × 2 matrix and B is a 2 × 3 matrix, so this a 3 × 2 matrix. Recall that taking a scalar multiple of a matrix does not change the dimensions of the matrixwill also be a 3 × 2 matrix. Therefore it may be possible to find values of a, b and c for which A = 2B . (If the dimensions of B were not the same as the dimensions as A then it would not be possible for 2B T to be equal to A.) We need to find and then 2B . For B T we simply interchange the rows and columns of B. And then for 2B we multiply each entry of Bby 2. We get: ▯ ▯ 1 c 1 c 2(1) 2(c) 2 2c B = 1 a b ⇒ B T = a 2 ⇒ 2B T = 2 a 2 = 2(a) 2(2) = 2a 4 c 2 −1 b −1 b −1 2(b) 2(−1) 2b −2 Comparing this last matrix to matrix A, we see that all of the known values match. That is, both matrices have 2 has their (1,1)-entry, 4 as their (2,2)-entry and −2 as their (3,2)-entry, so it will be possible to find values of a, b and c which make these matrices equal. (If there was any entry for which known values in the 2 matrices were not identical, then it would not be possible for the matrices to be equal.) 2 3 2 2c We need to have −1 4 = 2a 4 , so it must be true that 2c = 3, 2a = −1 and 2b = 0. 0 −2 2b −2 We see that we need c =2, a = −2and b = 0. 96 Unit 7 Example 7.4. Find the sum of matrices A and B, if possible, in each of the following. ▯ ▯ ▯ ▯ 2 −1 3 1 5 0 (a) A = B = 0 2 5 −2 4 −6 ▯ ▯ ▯ ▯ −2 3 1 3 −2 (b) A = 1 4 B = −2 1 −3 T ▯ ▯ (c) A = 0 − B = 2 7 −4 (a) Recall that in order to add two matrices they must have the same dimensions. Since A is a 2×3 matrix and B is also a 2×3 matrix, the sum A+B is defined. Also recall that the sum of two matri- ces is the matrix whose entries are the sums of the corresponding entries of the two matrices. We get ▯ ▯ ▯ ▯ ▯ ▯ ▯ ▯ 2 −1 3 1 5 0 (2 + 1) (−1 + 5) (3 + 0) 3 4 3 A + B = 0 2 5 + −2 4 −6 = (0 − 2) (2 + 4) (5 − 6) = −2 6 −1 (b) This time, A is a 2 × 2 matrix while B is a 2 × 3 matrix. Matrix addition can only be per- formed when the matrices to be added have the same dimensions, so in this case A+B is not defined. (c) We see that A is a 3×1 column vector. And sinis a 1×3 row vector, then so andB therefore B is a 3 × 1 column vector. (Notice: The transpose of the transpose of a matrix is just the original matrix. So B = (B ) .) Therefore it will be possible to add A and B. But of course, we need to find B. Recall that the negative of a matrix can be obtained by changing the sign of each entry in the matrix. And of course the negative of the negative of a matrix is just the original matrix (i.e. −(−M) = M for any matrix M). So here= −(−B ). T ▯ ▯ T ▯ ▯ ▯ ▯ −B = 2 7 −4 ⇒ B = − 2 7 −4 = −2 −7 4 ⇒ B = −7 Now that we have found B (which is, as we knew it would be, a (3 × 1) matrix, so that it can be added to A), we find A + B: 5 −2 5 − 2 3 A + B = 0 + −7 = 0 − 7 = −7 −3 4 −3 + 4 1 Notice: We could have done this more directly as follows, using the fact that the transpose of the transpose of a matrix is the matrix itself. (That is, if we switch the rows and columns, and then switch them again, we have just put them back where they were in the first place.) So we can consider B as (B ) , and of course adding can be considered as subtracting the negative of the matrix, and to subtract one matrix from another we just subtract the corresponding components. Furthermore, whether we change the signs of a matrix before or after transposing it clearly makes no difference. That is, (−= −(B ), so we have T T T T A + B = A − (−B) = A − [−(B ) ] = A − (−B ) Therefore to add A and B we can subtract the transposefrom A: 5 5 2 5 − 2 3 T T ▯ ▯T A+B = A−(−B ) = 0 − 2 7 −4 = 0 − 7 = 0 − 7 = −7 −3 −3 −4 −3 − (−4) 1 Unit 7 97 Example 7.5. Given A and B as follows, find (a) 3A − B and (b) (2A − 3I + B ) . ▯ ▯ ▯ ▯ 1 2 1 2 A = B = 3 4 −2 0 (a) Notice that since A and B are both 2 × 2 matrices, the stated operations are all defined. We find 3A by multiplying each element of A by 3, and then subtract B by subtracting corresponding ▯ ▯ ▯ ▯ ▯ ▯ ▯ ▯ 1 2 1 2 3(1) 3(2) 1 2 3A − B = 3 − = − 3 4 −2 0 3(3) 3(4) −2 0 ▯ ▯ ▯ ▯ 3 − 1 6 − 2 2 4 9 − (−2) 12 − 0 11 12 (b) Recall that I is an identity matrix, i.e. a square matrix whose main diagonal elements are all 1’s and whose off-diagonal elements are all 0’s. Since I here appears in a sum/difference of 2 × 2 matrices, clearly i2 is I , i.e. the identity matrix of order 2, which is meant. (That is, we assume that I here means the particular identity matrix for which the required calculation is defined.) We start by finding the matrix whose transpose will be the final answer. That is, we can find 2A − 3I + B , and then take the transpose of that matrix to get (2A − 3I + B ) . We have: ▯ ▯ ▯ ▯ ▯ ▯T 2A − 3I + BT = 2 1 2 − 3 1 0 + 1 2 3 4 0 1 −2 0 ▯ ▯ ▯ ▯ ▯ ▯ = 2 4 − 3 0 + 1 −2 6 8 0 3 2 0 ▯ ▯ ▯ ▯ = 2 − 3 + 1 4 − 0 + (−2) = 0 2 6 − 0 + 2 8 − 3 + 0 8 5 Therefore (2A − 3I + B ) = 0 8 So far we have mostly been dealing with arithmetic operations for matrices which are very similar to the corresponding arithmetic operations for vectors. But with matrices, there is also a multipli- cation operation defined. Recall that with vectors, we don’t have a multiplication operation. We do have two different kinds of products, the dot product and the cross product, but neither of these is considered to be multiplication, so for vectors there is nothing that directly corresponds to multi- plication. And the dot product operation for vectors is not one which could easily and directly be extended to the context of matrices. Also, the cross product is only defined for vectors in ℜ , so it is very exclusive and cannot be extended to matrices. However, part of the multiplication op- eration for matrices will look very familiar, because it does involve what is effectively the dot product. Matrix multiplication is more complicated than the other matrix operations that we’ve looked at so far. It’s not hard, just somewhat more complicated. Once you get the hang of it, it’s easy. But let’s work up to it gradually, to make sure you remember the steps. First, we’ll look at the rules about which matrices can be multiplied together?. 98 Unit 7 Definition: Consider 2 matrices A and B. The matrix product AB is only defined if A is an m × n matrix and B is an n × p matrix. That is, two matrices can be multiplied together only when the number of columns in the first matrix of the product is the same as the number of rows in the second matrix of the product. Well, that’s probably not what you were expecting! It seems a little quirky, but it’s not that hard a rule. And there’s a good reason for it. Once we learn how to calculate a matrix product, you’ll see why we need those dimensions to match. And then it will be easy to remember, because if they don’t match, you won’t be able to calculate the entries of the product matrix. You can think of it as the “inner” dimensions of the product. That is, if we multiply an m × n matrix times an n × p matrix, we’re doing (m × n) × (n × p) and it’s those two inside dimensions, that are right next to each other but from different matrices, that have to be the same. (Of course, when we say (m × n) × (n × p), the middle × doesn’t mean the same thing that the other two do. But the fact that it looks the same is kind of helpful. Or we could write it as (m×n)▯(n×p), because sometimes we use ▯ to represent multiplication. And using the ▯ might be even better, to help you remember what to do ... but we’re not there yet.) So for instance, if A is a 2 × 3 matrix, and B is a 3 × 2 matrix, then we can form the matrix product AB, because (2×3)×(3×2) has the 2 inner dimensions matching. We can always mutliply a “something” by 3 times a 3 by “anything”. Likewise, we can multiply a 3 × 2 times a 2 × 3, so the matrix product BA is also defined. However, the products A(B ) and (A )B are not defined, because for A(B ) we’re trying to multiply a 2 × 3 times a 2 × 3, and for (A )B we’re trying to multiply a 3 × 2 times a 3 × 2. In both of those, the number of rows in the second matrix is not the same as the number of columns in the first matrix. And now, suppose that we also have C, which is a 2 × 2 matrix. Then we can use C in a matrix product as the first matrix if it’s multiplying a matrix that has 2 rows, or as the second matrix in the product if it’s being multiplied by a matrix that has 2 columns. So the matrix product CA is defined (i.e. (2 × 2) × (2 × 3) works) and the matrix product BC is defined (i.e. (3 × 2) × (2 × 2) works). But the matrix product AC is not defined (because (2 × 3) × (2 × 2) doesn’t match) and neither is the matrix product CB (because (2 × 2) × (3 × 2) doesn’t match either). On the other hand, the products (A )C and C(B ) are defined. A couple of notes about notation 1. We always just write the names of the matrices beside each other to express a matrix product. We don’t use a × or a ▯ to indicate that we’re multiplying. Just the same as with unknowns. We never write x × y, we just write xy to say x times y. With numbers, we need a multiplication symbol between them, or brackets, because two number written beside each other means something else ... another number. (e.g. if we write 62, that doesn’t mean 6 times 2, it means sixty-two.) But if A is a matrix and B is a matrix, then AB never means anything but A times B, so we don’t need a symbol to say “times”. 2. When we write a T to indicate the transpose of a matrix, it always means just the matrix it’s attached to, i.e. right beside. So we don’t usually write something like A(B ). There’s no need for the brackets. We just write AB T and we know that it means A times the transpose of B, because the is on the B. If we wanted to say “the transpose of the product matrix AB”, then we would have to write it as (AB) . We need the brackets, so that the transpose can be “attached” to the brackets to show that it’s the whole thing inside the brackets that is being transposed. Unit 7 99 Example 7.6. Consider the matrices shown here: ▯ ▯ ▯ ▯ 5 1 0 −2 5 A = 2 −1 3 B = −2 3 C = 0 D = 0 3 4 −1 0 2 5 1 4 −3 5 −1 2 4 How many different matrix products of the form M 1 a2e defined, where each of M an1 M is 2 either one of the given matrices or the transpose of one of the given matrices? A is a 2×3 matrix, so A is a 3×2 matrix. Both B and B T are 2×2 matrices. C is a 3×1 matrix and D is a 3 × 4 matrix, so Cis a 1 × 3 matrix and D is a 4 × 3 matrix. Let’s consider the matrices, one by one, as the first matrix in the product, and see which of the 8 matrices could be the second matrix in the product. We can form a matrix product of the form AM for any matrix M which has 3 rows, i.e. as long as M is a 3 × n matrix for any value n. Therefore the products AA , AC and AD are all defined. For the matrix product BM, M must be a 2 × n matrix. A satisfies this requirement, as do B itself, and its transpose, so the products BA, BB and BB are all defined. For CM we would need M to be a 1 × n matrix. Only C meets this requirement, so the only product of this form which is defined is CC . And DM requires that M be a 4×n matrix, which only describes D , so DD is the only product with D as the first matrix. Of course, we could also have a transposed matrix as the first matrix in the product. For A M we need M to be a 2×n matrix, and that means that A A, A B and A BT T are all defined. Since B is a 2 × 2 matrix, we can again have any of those same matrices as the second matrix in a product B M, so B A, B B and B B T T are defined. C M needs M to be a 3 × n matrix, so C C, C DT T T T and C A are all defined. Similarly, since also has 3 columns, it can multiply any of those same matrices, that all have 3 rows, so D C, D D and D A T are all defined. Using only these 4 matrices and their transposes, any of 20 different matrix products can be formed. Notice: For any matrix M, if M is an m × n matrix, then MT is an n × m matrix, so both MM T T T T and M M are defined. And if M is a square matrix, then both MM and M M are also defined. Okay, so we know which matrix products are defined. But what do we get when we multiply one matrix by another? That is, if the matrix product AB is defined, what does it produce? Well, it gives a new matrix. And the 2 inner dimensions, that are the same, collapse in on themselves and disappear, as we see in the following. Definition: If A is an m×n matrix and B is an n×p matrix, then the product matrix AB has dimensions m×p. That is, multiplying and m×n matrix times an n×p matrix produces an m × p matrix. For instance, if we multiply a 3 × 4 matrix times a 4 × 2 matrix, we get a 3 × 2 matrix. If we multiply a 2 × 1 matrix times a 1 × 2 matrix we get a 2 × 2 matrix, but if we reverse the order of the matrices in the product, so that we’re multiplying a 1 ×2 matrix times a 2× 1 matrix, we get a 1 × 1 matrix, i.e. a matrix containing only a single number. Example 7.7. Recall the matrices defined in Example 7.6. Which of the matrix products identified in that example as be

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Students become familiar with the rules that governs the use of hyphens marks in well-written sentences. They develop basic skills in the use of hyphens in well written sentences, and practice using hyphens in various writing situations. 20 Views 16 Downloads - Activities & Projects - Graphics & Images - Lab Resources - Learning Games - Lesson Plans - Primary Sources - Printables & Templates - Professional Documents - Study Guides - Writing Prompts - AP Test Preps - Lesson Planet Articles - Interactive Whiteboards - All Resource Types - Show All See similar resources: Semicolons, Colons, and Hyphens In this using semicolons, colons, and hyphens worksheet, students read about their usages and apply the information by adding them to sentences, using colons or semicolons to join groups of words in two separate columns, and choosing... 4th - 6th English Language Arts Daily Warm-Ups: Grammar and Usage If grammar practice is anywhere in your curriculum, you must check out an extensive collection of warm-up activities for language arts! Each page focuses on a different concept, from parts of speech to verbals, and provides review... 3rd - 6th English Language Arts CCSS: Adaptable Grammar, Usage, and Mechanics If you're planning on teaching grammar in your fifth or sixth grade class, take a look at a packet of language arts activities that would be perfect for any grammar lesson. Covering skills such as parts of speech, sentence and paragraph... 5th - 6th English Language Arts CCSS: Adaptable Hyphens and Capitalization in Headings This is more than a activity, this is a full college style list of all the rules related to hyphens and capitals one would need to write excellent papers. You can use this resource to inform your own writing, or to enhance your learner's... 3rd English Language Arts

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