Pi Day Activities for the Classroom

Everyone loves pie, but we also love Pi. Used to calculate the width of a circle, Pi is an infinitely-long number derived from complex mathematical computations. Most of us remember that Pi is close to 3.14, but many others pride themselves on remembering the first 39 digits, which is how many you need to properly calculate the spherical volume of the universe. The numbers rise to stardom seems to have come from its challenge to memorize those 39 digits, as well as the fact that is has what many of us can agree might be the best homonym, pie. Pi enthusiasts have come to embrace March 14 as Pi Day, 3.14, a unique holiday which has launched numerous educational (not to mention delicious) ways to celebrate. Some of math teachers at Milken Community Schools in Los Angeles helped me assemble a list of some of the most popular (and yummy) ways to celebrate Pi Day. Check out our list of ideas for Pi Day Activities for you to do at home or in the classroom. Pi Plates Memorizing 39 digits of Pi can be quite the challenge, and a great way to get students thinking about those numbers can be to use Pi Plates. Using paper plates, write one digit on each plate and pass them out to students. As a group, they can work together and try to get all the numbers into the right order. For younger students, teachers may wish to only use 10 digits of Pi to make the activity a little easier. Make sure you have some painter’s tape for adhering them to wall without damaging the paint, or you can line them up in the hallway. You can even turn this into a competition between classes or grades, by asking each teacher to time her students to see how long it takes for them to get all 39 digits in the right order. What does the winner get? A pie, of course. Pi-Loop Chains Pull out the arts and crafts supplies, because this activity requires scissors, tape or glue, and construction paper. Using a different color for each digit of Pi, students can create a paper chain to use to decorate the classroom. See how many digits your class can calculate! Pi Pie This may be one of the most beloved ways to celebrate Pi Day. Baking a pie and using the dough to spell out the 39 digits of Pi as part of the crust has quickly become a tradition at many schools. At Milken School, some of the Upper School math teachers definitely enjoy having students bring in pies to celebrate, also hosting a small party which might include some special logic puzzles to kick off the class. Pizza Pi Not everyone has a sweet tooth, so another yummy way to celebrate Pi Day is with a different type of pie, a pizza pie! If your classroom has a kitchen (or access to one) students can calculate Pi for all the circular ingredients, including the pizza dough, pepperonis, olives, and even the pizza pan itself. To top it off, students can write out the symbol for pie using their circular pizza toppings.   Pi Trivia or Scavenger Hunt Set up a trivia game that asks students to compete against each other to correctly answer questions about Pi mathematicians, the history of Pi, and the uses of the famous number in the world around them: nature, art, and even architecture. Younger students might engage in a similar activity that focuses on the history of Pi by taking part in a scavenger hunt around school to find clues to these same trivia questions. Pi Philanthropy Math classes might want to celebrate Pi Day with a more philanthropic approach. According to one teacher at Milken, there are several ideas that a classroom might consider. Baking Pi Pies and selling them at a bake sale to benefit a local charity, or donating Pi Pies to a local food bank or homeless shelter can be a sweet treat for those in need. Students can also hold a food drive challenge, aiming to gather 314 cans of food for each grade level. Bonus points if you can convince your teacher or principal to reward students for reaching that goal by agreeing to receive a whipped cream pie to the face! Simon Says Pi This is a great little game for learning and memorizing the various digits of Pi. You can do this one student at a time in front of the whole class or in groups as a way to challenge each other to remember the digits of Pi and see who gets the farthest. Whether you’re doing one student at a time or breaking off into pairs, the person acting as â€Å"Simon† in this activity will have the number printed out on a card in hand, to ensure that the correct digits are being repeated, and will read out the digits, starting with 3.14. The second player will repeat those digits. Each time â€Å"Simon† adds a number, the second player must remember and repeat all the digits that were read aloud to them. The back and forth play continues until the second player makes a mistake. See who can remember the most! As an added bonus, make this an annual activity and you can create a  special  Pi Hall of Fame to honor the student who remembers the most digits each year. One school in Elmira, New York, Notre Dame High School, reportedly had one student remember 401 digits! Incredible! Some schools even suggest having different levels to honor how far students can go when it comes to memorization, with named groups to honor students who can remember 10-25 numbers, 26-50 numbers, and over 50 numbers. But if your students are recalling over 400 digits, you may need more levels than just three! Pi Attire Don’t forget to get all decked out in your very best Pi attire. Pi-tire, if you will. Teachers have long amused their students with math-themed shirts, Pi ties, and more. Bonus points if the entire math department participates! Students can get into the mathematical magic and don their own Pi digits as part of their outfits. Math Names One teacher at Milken shared this Pi-tastic tid-bit with me: â€Å"My second child was born on Pi Day, and I made his middle name be Matthew (aka, MATHew).†

Edexcel Igcse Economics Answer - 49663 Words

Answers: Section A: The Market System Chapter 1 (a) In all of the photographs goods are being traded. In A, people are buying goods from market traders in a souq. In B, goods are being sold by auction. In C, shoppers are buying goods from a supermarket. And finally, in D, cars are being bought at a car lot. (b) In C, shoppers queuing at a checkout will pay the price that is displayed on the labels of products (or at the point of sale). Shoppers will either pay the price shown or choose not to buy the various products. In D, the price is determined through negotiation between the car salesperson and the buyer. There is likely to be a price displayed for the car but this is usually a starting point for negotiations to begin. The†¦show more content†¦Demand is forcing up the price. On the other hand, if there are only a few bids this means that demand is low and the price of the product will also be low. If there are no bids at all this means that there is no demand and the product will go unsold. Sometimes on eBay there may be lots of people selling the same or very similar products. This means that supply is high and the effect will be to lower prices. Chapter 2 Getting started: (a) According to the table, when the price of fleeces is $50, 5,000 fleeces will be purchased per week. (b) As the price of fleeces goes up the number purchased per week falls. For example, when the price is increased from $50 to $70 the number of fleeces likely to be purchased falls from 5,000 to 3,000. (c) When the price of fleeces is lowered, the number purchased per week rises. For example, if the price is reduced from $50 to $40 the number of fleeces likely to be purchased rises from 5,000 to 6,000. Question 1: (a) If the rugby union club charges 40 Euros for a fixture, the attendance would be 5,000. (b) To fill the stadium the price must be set at 10 Euros. At 10 Euros 30,000 spectators would be attracted. This is full capacity. Exam practice – The Byron Bay Surf Shack: (a) Effective demand shows how much would be bought (i.e. how much people can afford to buy and would actually buy) at any given price. It does not mean how much people would like to buy

Car Manufacturing Companies in Australia-Free-Samples for Students

Question: Discuss about the Costs of Production in Manufacturing Industry in Australia. Answer: The article is discussing challenges car manufacturing companies such as Mitsubishi, Ford, Holden, and Toyota are facing in Australia. These companies want to move their assembly line to other countries due to the high cost of production in Australia. The stakeholders in this issue are of course car manufacturing companies, suppliers, tens of thousands of Australians who will lose their jobs as well as the Research and Development (RD) sector that is greatly influenced by the motor vehicle industry. The higher cost of production in Australias car manufacturing industry is due to several things (Valadkhani, 2016). These car manufacturing companies are looking to move into cheaper production inputs overseas including both labor and parts because the countrys market is not sufficiently large which makes it impossible for the manufacturing industry to exploit the economies of scale fully. Australias domestic market is weak due import tariffs that are too low as well as Free Trade Agreements; unions asking for higher wages and better working conditions; the appreciation of the Australian dollar. The cost of production in the car manufacturing industry in Australia cannot be compared to that of countries in Asia especially when it comes to labor costs. The article is very simple and focused which makes it easy to understand the different issues it is discussing, issues that are often difficult to identify in other articles because they are too focused on painting the car manufacturers as the evil ones for wanting to exit the Australian market. The whole point of the article is, car manufacturers such as Mitsubishi, Ford, Holden, and Toyota want to exit the Australian market because the opportunity cost of operating in the country is way too high. If this happens, a lot of people will lose their jobs which will significantly affect the unemployment rate regarding supply and demand as workers will be available but employers will be limited (Sherk, 2013). The Australian government is too focused preventing monopolies and unfair practices that it has developed unnecessary regulations and quotas that have interfered with the natural process of equilibrium that is supposed to exist in a perfectly free market and has resulted in inefficiency that could have easily been avoided. Further, the Australian government seems to be taking the comparative advantage approach with too low import tariffs and too much free trade agreements which greatly put car manufacturers at a disadvantage. Another problem involves the companies variable costs most especially when it comes to labor. Labor unions are asking for unreasonably high wages and conditions that do not correspond with the companies level of output. This situation resembles that of a monopoly because labor unions are selling labor to these companies at a very high price, prompting them to hire less labor than they would in equilibrium which affects their production capabilities (Library of E conomics and Liberty, n.d.). The appreciation of the Australian dollar is another problem that is making exporting parts more expensive and imports way cheaper due to lower inflation. The appreciated Australian dollar has also caused a fall in the domestic Aggregate Demand (AD) due to lower demand in exports and greater spending on imports. As a result, it has slowed the market growth in the country which has prevented car companies from fully exploiting economies of scale. There are various things that the car manufacturing companies could do to reduce the cost of production without withdrawing from the Australian market. The cost of production can be reduced by decreasing the number of platforms (critical structures in forming the base of various automobile models) that are used in producing vehicles. Producing a greater number of models using a common platform will considerably reduce the high number of expenditures that designing and developing multiple platforms would require (Sedgwick, 2014). Further, producing on a larger scale will reduce the manufacturing cost per vehicle. Car manufacturing companies could also develop strategies that will increase the commodities of parts and components used in their vehicle models including decreasing model variations as well as the number of parts that are used in their models. Further, adopting the design approach where associated parts are treated integrated systems could also comprehensively reduce produc tion costs. The government needs to intervene and support the car manufacturing industry which will give car manufacturer additional power in order to get rid of the unsustainable wages and conditions set by the unions through negotiations or by taking the matter to the Federal Court. Another way the government could intervene is by backing these companies in the creation of their union and increase subsidies which will secure the future of the car manufacturing industry as it is too important to let go. Another way the government could support the can manufacturing industry is offering tax incentives such as tax deductions on Research and Development (RD) and exports (Davison, 2013). This article is very useful; it is opening peoples eyes on what is happening with countrys economy. It would be disastrous if these companies were to go through with their decision of leaving the Australian car manufacturing industry. A lot of peoples livelihoods in Australia depend on manufacturing companies like Mitsubishi, Ford, Holden and Toyotas capabilities to stay in operation. That would not be possible if domestic market conditions in Australia remain unsustainable. The car manufacturing industry is Australia does not have productivity problem, it has an immeasurable cost barrier that the government seems to be contributing to by setting import tariffs that are too low and signing too many Free Trade Agreements that do not make a lot of difference to exports because of internal tax exercises (Kohler, 2013). The appreciation of the Australian dollar does not help things either especially when it comes to imports and exports; exporting parts will be too costly for these companies which will make their products too expensive for consumers; as a result, they are turning to imported products that are cheaper. Australia is simply too expensive to operate in so it makes sense for these companies to look elsewhere for better conditions. However, this event would not be good not only for the employment rate but for other sectors such as the Research and Development sector that work hand in hand with the car manufacturing industry. References Davison, R. (2013). Fact Check: do other countries subsidize their car industry more than we do?. Retrieved from https://theconversation.com/factcheck-do-other-countries-subsidise-their-car-industry-more-than-we-do-16308 Kohler. A. (2013). Subsidizing the car industry to death. Retrieved from https://www.abc.net.au/news/2013-10-16/kohler-car-industry/5025360 Library of Economics and Liberty. (n.d.). The 51 Key Economics Concepts. Retrieved from https://www.econlib.org/library/Topics/HighSchool/KeyConcepts.html Sedgwick, D. (2014). Carmakers bet on big global platforms to cut costs. Retrieved from https://www.autonews.com/article/20140804/OEM10/308049988/carmakers-bet-on-big-global-platforms-to-cut-costs Sherk, J. (2013). Supply and Demand: Why Job Growth Remains Sluggish. Retrieved from https://www.heritage.org/jobs-and-labor/report/supply-and-demand-why-job-growth-remains-sluggish Valadkhani, A. (2016). Collapse of Australian car manufacturing will harm RD in other sectors: study. Retrieved from https://theconversation.com/collapse-of-australian-car-manufacturing-will-harm-randd-in-other-sectors-study-66984

Sup. Natl In Macbeth Essays - Characters In Macbeth,

Sup. Nat'l In Macbeth ?Supernatural Forces in Macbeth? In Shakespeare's Macbeth, specific scenes focus the readers' attention to the suspense and involvement of the supernatural. The use of witches, apparitions and ghosts are an important element in making the play interesting. Examining certain scenes of the play, it can be determined that as supernatural occurrences develop, Macbeth reflects a darker self-image. Macbeth experiences his first strange encounter of the supernatural when he meets the three witches in act one, scene one. After learning of his prophecies to become king, Macbeth states, ?Glamis, and Thane of Cawdor: The greatest is behind (still to come).? (1.3.117-118). Shakespeare uses foreshadowing, a literary technique, to suggest to his readers the character Macbeth will suffer a personality change. Macbeth also implies his first notions of plotting an evil scheme by this comment. After the prophecies of the witches revealed the fate of Macbeth, the quest of the throne will be his next vi ctory. ?The witches reveal a fate for Macbeth and imply that a part of what will come to him must come, but they reveal no fate of evil-doing for him and never, even by suggestion, bind him to evil doing. ?, states literary critic Willard Furnham. Furnham declares the only power the witches obtain over Macbeth, is the power of insinuation. By offering to Macbeth the idea of power, the witches push Macbeth to the next level of greed and evil which was non-existent prior to the encounter. The murder and death of King Duncan initiates Macbeth's second encounter with the supernatural when he witnesses a floating dagger. As Macbeth awaits the signal to make his way up the stairs, he sees the floating dagger and proclaims, ? Come, let me clutch thee. I have thee not, fatal vision, sensible (able to be felt) to feeling as to sight, or art thou but a dagger of the mind, a false creation, proceeding from the heat-oppressed brain (2.2.33-38). This apparition confuses and frightens Macbeth. He can not comprehend how he can see something and not be able to touch it. ?Thou leads me the way I was going; and such an instrument I was to use. And on thy blade and hilt, drops of blood which was not so before. There's no such thing. It is bloody business which takes shape.? (2.2.43-49) Here, Macbeth begins to question whether his mind is playing tricks on him. The situation seems quite coincidental considering he is minutes from murdering a man with a similar weapon. He states the apparition is due to the bloody business about to occur. The dagger symbolizes the point of no return for Macbeth. If he chooses the path in which the dagger leads, there will be no turning back. Macbeth fears Banquo for his prophecy is to father kings, so Macbeth proceeds to plot the murder of his once friend, which spurs yet another brush with the supernatural. Macbeth attends a banquet at which he witnesses the ghost of his dead friend. (3.4.37-145) The fortunes of the three witches sparked Macbeth' s desire to murder Banquo and caused him to dig himself into a deeper hole. Macbeth's guilt and fear combined drive him to darker and more evil actions in an attempt to cover his past misdeeds. ?What man dare, I dare. Approach though like the rugged Russian bear, the armed rhinoceros, or th' Hyrcan tiger; Take any shape but that (Banquo) and my firm nerves shall never tremble.? (3.4.100-104) Macbeth is terribly frightened by the bloody ghost haunting him and is angered that the ghost revealed it self to him. His guilt causes him to proclaim he could take on a rhino, tiger or any other wild animal, but not Banquo's ghost. After his encounter with the ghost, Macbeth proceeds to visit the witches one last time to insure his security. After this last visit, Macbeth becomes overconfident and a tyrant, which cause his downfall. The use of supernatural in Macbeth, is a major factor in the suspenseful nature of his work. Without the witches, apparitions and the ghost, Macbeth could not have reached his downfall. The use of supernatural in Macbeth caused Macbeth to become a darker and more evil person with each