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Algebra is the first “real” course in mathematics. Based on the principles of arithmetic that you have already learned, Algebra uses symbols to create generic solutions that work in a variety of cases.
This class is now taught by Mr. Tregembo using the Glencoe Algebra 1 book. This book is available on disk, with tutorials for use by students and parents. Shearer for a copy of the student disk. The book is also available on-line. Shearer for the web site, log-in name, and password. For those students and parents who are interested, Mrs. Shearer provides Math Help in her classroom before school or after school.
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You do not have to be taking a math class from Mrs. Shearer to come for Math Help. In Algebra 1 you will learn how to use the rules of arithmetic to solve a variety of equations. You will learn how to draw graphs of straight lines and parabolas.
You will learn about the shapes of graphs for many types of equations. Algebra also includes some statistics and probability and a small amount of geometry. Throughout these web pages, be sure to click on the highlighted terms and topics to find out more. Here is what you can find out about Algebra on this page:. So what is algebra? Algebra is a way of generalizing arithmetic.
It uses letters called variables to represent any value in a given formula so that it becomes a general formula that can be applied to all numbers. In fact, you don’t have to use letters – you could use symbols or pictures if you wanted. But most math people are so lazy they don’t want to do that much work – letters are easier.
If we let the letter a stand for anything and a little dot stand for multiply so we can know it is not the letter X we can write an equation that is always true:. Early mathematicians found that using letters to represent quantities simplified the problems.
It is one way to get rid of all the words in a word problem. In Algebra I we only study problems that use the real number system. Just like it sounds, it is a bunch of numbers that we use in real life and it excludes only the imaginary numbers imaginary is not real – get it? So what is included in the real number system? In elementary school you learned to count things. You can also use natural numbers to make lists.
Whole numbers act a lot like the natural numbers. Zero is used to indicate none or nothing. It might seem simple to have a number called zero, but it was never used by the Greeks or Romans.
Zero was used by Arab mathematicians – the same people who invented Algebra. For more about the history of zero, go to Wikipedia.
For computer people and some branches of mathematics, they usually start their lists counting notbles zero. Algebra problems often require you to round your answer to the nearest whole number. Integers broaden your number range a little bit.
They allow you to include all whole numbers and their opposites.
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The official way to read the sign in -5 is to say “negative 5”, but some people say “minus 5”. I sometimes confuse my students because I use both ways to refer to negative numbers.
Negative numbers are used a lot in real life. For example, if you drive to Albuquerque you have gone about miles. When you come home, you can think of it as driving miles negative milesthe opposite of going to Albuquerque. Be careful when working with negative numbers. The minus sign on a calculator is not the same as the subtraction sign, even though they look a lot alike. It is usually written – and can be found near the bottom of your calculator. The minus subtract sign is usually on the side of the calculator with the other aritnmetic operations add, multiply, and divide.
Rational numbers act rationally – they sort of make sense – at least they make sense to math people. Rational numbers are glenco you get when you divide integers by integers, so they can be either positive or negative.
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Rational numbers can be thought of as ratios or fractions. Rational numbers often are written as fractions, but they can also be decimals. In fact, every decimal that repeats, like 0. In all cases, rational numbers can be written as a fraction of integers.
Some examples of rational numbers includes all of the natural numbers 1, 2, 3. The last type of real numbers are called irrational. Irrational numbers cannot be written as a fraction. The decimal value for irrational numbers never end and never have a repeating pattern.
Examples are pi and the square root of 2. Be careful when working with irrational numbers on a calculutor.
The calculator is only giving you part of the answer and it is an estimate. Remember that all irrational numbers have a decimal part that goes on forever without repeating. Important vocabulary – in the book important words are highlighted in yellow. You should write these down in your Notables book or on a Foldable.
An English and Spanish glossary starts on page R1 after page that gives definitions and a reference back to a page in the book. The Glossary has purple edges on its pages. Many of the glossary words from your book are also listed here. Student Handbook – beginning on page with green edges on its pages, this provides a good review of things you should have learned in math before beginning Algebra 1. This section provides answers to odd problems for exercises, practice quizes, and the chapter reviews.
Use these to check your own work to make sure you understand how to do the assignments. Buttons created at ButtonGenerator.