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. 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