Introducing Integers and Rational Numbers to Students with Disabilities

Introducing Integers and Rational Numbers to Students with Disabilities Positive (or natural) and negative numbers can confuse students with disabilities. Special education students face special challenges when confronted with math after 5th grade. They need to have an intellectual foundation built using manipulatives and visuals in order to be prepared to do operations with negative numbers or apply algebraic understanding of integers to algebraic equations. Meeting these challenges will make the difference for children who might have the potential to attend college. Integers are whole numbers but can be whole numbers both greater than or less than zero. Integers are easiest to understand with a number line. Whole numbers that are greater than zero are called natural, or positive numbers. They increase as they move to the right away from the zero. Negative numbers are below or to the right of the zero. Number names grow bigger (with a minus for negative in front of them) as they move away from the zero to the right. Numbers growing larger, move to the left. Numbers growing smaller (as in subtraction) move to the right. Common Core Standards for Integers and Rational Numbers Grade 6, the Numbers System (NS6)Students will apply and extend previous understandings of numbers to the system of rational numbers. NS6.5. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.NS6.6. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.NS6.6.a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., (-3) 3, and that 0 is its own opposite.NS6.6.b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. NS6.6.c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Understanding Direction and Natural (positive) and Negative Numbers. We emphasize the use of the number line rather than counters or fingers when students are learning operations so that practice with the number line will make understanding natural and negative numbers much easier. Counters and fingers are fine to establish one to one correspondence but will become crutches rather than supports for higher level math. The pdf number line is for positive and negative integers. Run the end of the number line with positive numbers on one color, and the negative numbers on another. After students have cut them out and glued them together, have them laminated. You can use an overhead projector or write on the line with markers (though they often stain the laminate) to model problems like 5 - 11 -6 on the number line. I also have a pointer made with a glove and a dowel and a larger laminated number line on the board, and I call one student to the board to demonstrate the numbers and jumps. Provide lots of practice. You Integer Number Line should be part of your daily warm up until you really feel that students have mastered the skill. Understanding the Applications of Negative Integers. Common Core Standard NS6.5 offers some great examples for applications of negative numbers: Below sea level, debt, debits and credits, temperatures below zero and positive and negative charges can help students understand the application of negative numbers. The positive and negative poles on magnets will help students understand the relationships: how a positive plus a negative moves to the right, how two negatives make a positive. Assign students in groups the task of making a visual chart to illustrate the point being made: perhaps for altitude, a cross cut showing Death Valley or the Dead Sea next and its surroundings, or a thermostat with pictures to show whether people are hot or cold above or below zero. Coordinates on an XY Graph Students with disabilities need lots of concrete instruction on locating coordinates on a chart. Introducing ordered pairs (x,y) i.e. (4, -3) and locating them on a chart is a great activity to do with a smart board and a digital projector. If you dont have access to a digital projector or EMO, you might just create a xy coordinates chart on a transparency and have students locate the dots.

Top 11 Writing Apps for iOS (iPhone and iPad)

Top 11 Writing Apps for iOS (iPhone and iPad) Top 11 Writing Apps for iOS (iPhone and iPad) Top 11 Writing Apps for iOS (iPhone and iPad) By Daniel Scocco Finding the best writing apps for iOS can be challenging. Arguably the best word processor in existence, Microsoft Word, was designed with Windows in mind. Still, developers have answered the call and diehard Apple fans can still find several high-quality writing apps to help them write down their ideas. Whether you need a full-scale word processor or a simple notetaking app, there are several great options for iOS users. 1. Byword If you are writing on mobile or tablet, Byword is one of the best markdown editors out there. It isn’t flashy, it won’t cure cancer, but it will help you write down words. By default, it supports TXT, TEXT, MD, MMD, MARKDOWN, MARKDN, MDOWN, MKDN, MARKD, and Fountain file formats. Another added bonus of Byword is that you can export your finished products as PDFs and HTML documents. 2. Editorial Editorial comes with a little more functionality than Byword. What makes Editorial a great app is the fact that it has features like a built-in multi-tab web browser, Dropbox integration, and more. It also comes with inline preview for taskpaper, markdown, and foundation documents. 3. 1Writer 1Writer is one of the best notetaking apps for iOS. It can easily be downloaded from the App Store for either iPhone or iPad. The app can be used to write down ideas, for research, or to revise past ideas. 4. iA Writer Pro If you are looking for a great, free word processor, iA Writer Pro is the right app for you. This app provides you with all the tools and features you expect from a word processor without the price. By default, it is compatible with both the iPad and iPhone. 5. Pages Pages is Apple’s response to Microsoft Word. Like any app developed by a major company, Pages works as you would expect to. It is also completely compatible with iOS because it was designed specifically for it. Pages is great because it comes with every feature you will need as a writer. If you require a more professional-grade word processor, Pages is exactly what you need. 6. Ulysses What more could you expect from a program that was named after one of the greatest novels ever written? This word processor is compatible with most devices that run on iOS. Ulysses is considered to be one of the best writing apps on the App Store and is used by many professional writers who work on iOS. Why is Ulysses so good? It boasts a simple, yet effective design, is easy to use, has workflow options, a slew of export options, and syncs across the various iOS devices. 7. Werdsmith Werdsmith is another great option for aspiring writers who use iOS. This free app is compatible with both the iPhone and iPad. What makes Werdsmith great is the fact that it is loaded with features, has a great UI, Dropbox integration, and it can even be used on the iPod touch. 8. Bear Bear is another example of a barebones, markdown notetaking app. It won’t blow you away with features, but it does what it does well. This notetaking app is best used for taking notes and writing prose. You can also input your notes into Bear, making it a great app to use to study while you are transiting to and from school. Bear is very easy to use and a great option if you want a free notetaking app. 9. Microsoft Word for iOS Alright, you may be thinking, why are you suggesting Microsoft Word for iOS? One simple reason, because it exists. If you are comfortable with Microsoft Word and all of its features, why change? Microsoft has created an iOS version of their flagship word processor and it works flawlessly. A lot of iOS users make use of Pages because they think it is the go-to word processor for iOS. But, if Microsoft Word is available, why not use arguably the best word processor on the market? 10. Grammarly Sometimes Grammar is hard. Even the best writers will tell you this. Grammarly isn’t an official writing app like the other ones previously listed. Grammarly is a free grammar-checking app that is available on iOS. The free version will help you make basic corrections and improve your grammar, while the paid version comes with even more features. With Grammarly, you will never struggle with spelling, syntax, and sentence structure. 11. Dictionary.com App No one has perfect spelling. We all misspell words and rely on that wavy red line to tell us when we make mistakes. The official Dicitonary.com app is a great choice for writers who want to bolster their vocabulary, check the meanings of new words, and help find synonyms for words that they use too much. What makes this app even better is that it is free and it comes in a lite version. Want to improve your English in five minutes a day? Get a subscription and start receiving our writing tips and exercises daily! Keep learning! Browse the Freelance Writing category, check our popular posts, or choose a related post below:When to Use â€Å"That,† â€Å"Which,† and â€Å"Who†Yay, Hooray, Woos)

INTERNATIONAL BUSINESS FINANCE AND TRADE Essay Example | Topics and Well Written Essays - 3000 words

INTERNATIONAL BUSINESS FINANCE AND TRADE - Essay Example The Enron Corporation before its collapse was one of the largest global company which had its hands in the sales of natural gas and electricity, commodities like bandwidth internet connection and provided other financial and management services. Failure of corporate governance can be due many reasons. In financial terms if a company owes more than it earns over a significant time period and is not able to carry out trade then it faces a corporate failure. Failure can also occur due to institutional failure in which a group of managers fails to tackle major issues of the company. An important factor behind the collapse of corporate governance is the financial crisis. â€Å"The Enron failure demonstrated a failure of corporate governance, in which internal control mechanisms were short-circuited by conflicts of interest that enriched certain managers at the expense of the shareholders.† (Enron: Corporate Failure, Market Success, 2002). A complete reevaluation of corporate govern ance practice in the United States became important after the fall of Enron. The financial goals of a corporate sector are mainly maximization of share holder’s wealth and the maximization of corporate wealth. The wrong financial decisions taken by the authorities leading to a ‘dubious’ financial transaction also contributes to the failure of corporate governance. The free market situation which emerged as a result of liberalization and the process of privatization of public sector got questioned after the breakdown of the Enron. â€Å"The failure of the corporate governance system should be viewed as the failure of the corporate internal control system† (Dewan, 2006, P. 51 An effective system of corporate governance has both internal and external aspects that have to be sufficiently responsive if governance is to succeed. â€Å"Different internal and external influences address different issues within an organization† (Hafner, 2010, P. 6). Absence of an appropriate internal governance system which leads to an inefficient financial and management performance may also contribute to the breakdown of corporate governance as happened at Enron. Failure of External governance system which has the responsibility to warn the company about the future market situations to do its duty may also contribute to the failure of the corporate governance. The power in the hands of the company given by the corporate rules to influence the policy makers and hence the government has been another reason for the corporate failure. The collapse of corporate governance was not just rooted in poor managerial performance but the entire corporate department plays a major role in ruining the corporate ethical values and principles. But the primary responsibility for the failure of corporate governance lies with the executives and the managers. If the operations management were allowed to work according to the corporate norms then the tragedy of the Enron c ollapse might not have occurred. Effective regulation and oversight, restrictions on campaign financing, and an arms length approach of government in dealing with business may have prevented the breakdown of Enron. â€Å"Enron situation taught a lesson about the main reasons for such failures and not to repeat the same mistakes in the future. The Enron situation was the focus of a massive investigation that led to significant changes in corporate governa

Microbial Produced Fuels as Economically Viable Renewable Fuel Source Essay

Microbial Produced Fuels as Economically Viable Renewable Fuel Source - Essay Example The essay seeks to perform a brief overview of the existing microbiological means of energy production and creates a persuasive argument for furthering the research and funding into alternative fossil fuels. There are several different types of microbiological means of creating fuels. Many of these have been understood since the beginning of the 20th century; others have only recently been developed in the past decade or so. One of the oldest forms of creating energy via microbiological means is with regard to using different strains of bacteria to produce electricity. This particular practice was engaged as early as the late 1920s by teams of American and German scientists that were interested in the means through which electrical generation via natural and readily available cultures might exist. Not surprisingly, this particular form of electrical generation was extraordinarily inefficient and yielded only a very small amount of electricity as compared to the level of investment that it required to function. More recently, scientists have turned their collective energies towards the creation of gasoline derivatives and/or biodiesel through a process of photosynthesis and algae reproduction. The inherent benefit technology improvement has to do with the fact that if this particular process is perfected, the overall energy independence that a particular region or nation Hope to exhibit will be drastically increased. This technology does not exhibit any toxic or long-lasting negative impacts.

Compare racial and cultural struggles in Alice Walker’s The Color Essay

Compare racial and cultural struggles in Alice Walker’s The Color Purple as well as Toni Morrison’s The Bluest Eye. In African-American texts, blacks are seen as struggling with the patriarchal worlds they live in order to achieve a sense of Self and Identity. The texts I have chosen illustrate the hazards of Western religion, Rape, Patriarchal Dominance and Colonial notions of white supremacy; an intend to show how the protagonists of Alice Walker’s The Color Purple as well as Toni Morrison’s The Bluest Eye, cope with or crumble due to these issues in their struggle to find their identities. The search for self-identity and self-knowledge is not an easy task, even more so when you are a black woman and considered a mule and a piece of property. Providing an in depth analysis of these texts, this essay attempts to illustrate how both of these Afro-American writers depict and resolve their respective protagonists’ struggles. Religion is believed by many to serve as a means to achieving or finding self or identity. However, in the Euro-influenced Christian religion especially, directly after ‘finding one’s self’, one is called to deny one’s self in the name of a white ‘God’. ‘Humble yourself and cast your burdens to God’ they say, for ‘He will make all wrongs right’. Logically however, one must ask†¦what interest does the white God (who is especially portrayed in Afro-American writings such as The Color Purple and The Bluest Eye as a further extension of Patriarchal values) have in black people? Moreso, if the Christian bible is so heavily influenced by white man, what interest does the God it portrays have in black women? In The Color Purple, Celie’s original intended audience is a white, male God w... ... the voiceless, to overcome the patriarchal oppression and gradually find her ‘Self’. Bibliography Cutter, Martha. Philomela Speaks: Alice Walker's Revisioning of Rape Archetypes in The Color Purple - Critical Essay. MELUS, Fall – Winter, 2000. Davis, Thadious M. Walker’s Celebration of Self in Southern Generations. Hooks, Bell, ‘Writing the Subject: Reading The Color Purple’, in Bloom, H., ed. Modern Critical Views: Alice Walker, New York, 1989. Katz, Tamar. â€Å"Show Me How to Do Like You.† Didacticism and Epistolary Form in The Color Purple. 1988. Morrison, Toni The Bluest Eye, London: Picador, 1990. Peach, Linden Toni Morrison London: MacMillan, 1995. Shakhovtseva, Elena.  «The Heart of Darkness » in a Multicolored World: The Color Purple by Alice Walker as a womanist text. Walker, Alice The Color Purple London: The Women’s Press, 1986.

The Impact of Advertising on Graffiti

In an era defined by hyper reality, branded lifesylfe, and instant gratification. Effect= noun Is graffiti a direct result of advertising? To evaluate how the advertising industry has played a role in the inception of street art sub culture, we must compare each institution’s role in society, the techniques employed (use of propaganda) by each, and how past artistic movements have been influenced by forces that propel them into. Commercial consumer advertising is propelled by immediate financial profit and mediated by boardrooms and stockholders.It aims at exposing that product in an appealing way, and doing it so as many people are aware of that product. Graffiti is a tool used by individuals with their own agenda, one however that doesn't include profit as its foremost target. The main agenda of a graffiti artist is exposure by means of guerrilla tactics. To understand how advertising has contributed to the establishment of graffiti subculture, the roles each has in society must be examined. Advertising has come a long way from the archaic methods of attraction. Long gone are the times of fact-based advertising.Instead we have moved on to the aesthetisation of commodities, and consequently a world in which the promise made by the seller of love, eternal youth and a perfect body turns people into obsessive-compulsive consumers with a proclivity for instant gratification and a 5-second attention span. The advertising industry sells a way of life, not a product; in fact the ad itself becomes the object of aesthetisation. Over time advertisements have become much more than just ads, they incorporate art of all kinds to appeal to all tastes, using strong cultural signifiers that evoke certain emotions in the viewer.They are like an exact science; they employ psychologists, behaviorists, and all kinds of experts from different fields to pinpoint the moment when a mind will be ready to respond to all these messages. Graffiti becomes a visual manifestation of man's desire to leave his mark on the world, something that is the hallmark of advertising practice, while visually (logos, signs, brands), advertising has provided the ‘raw materials' as it were, with which writers become known. advertising and a world over-saturated with popular culture imagery

Teaching Methods For Students With Disabilities Essay

Introduction: In recent decades, more and more schools are including special education in a general classroom setting. The subject of this inclusion has been placed on the forefront of not only the educational system but also on public consciousness. Still, there are debating questions that plague this very subject. What teaching techniques are being implemented to include students with disabilities in a general education setting? Many techniques have been implemented in the attempts to include students with disabilities. Some have been successful and some have not. However, there are many techniques that needs to be explored, researched and thus implemented especially if the educational system expects this integration to be fruitful for all involved. Inclusion in classrooms are important in order to establish diversity that stems beyond cultural and religious affiliation. Diversity also includes students with physical and learning disabilities. Learning acceptance of diversity early in educational setting will foster positive attitudes towards peer development and will also enhance a positive outcome for students in need of special education. Attitudes from both aspects of the spectrum needs to be adjusted to accommodate these necessary changes within the educational system. Define the Construct: As previously mentioned, diversity plays an important role in the success of inclusion for all students. 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