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. Contact Mrs. Shearer for a copy of the student disk. The book is also available on-line. Contact Mrs. 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. 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:

- What is Algebra
- Numbers used in Algebra
- What is in your textbook
- Topics in Algebra
- Examples in Algebra based on e-mail from students

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

Example – you all know that when you multiply **anything**
times zero the answer is always zero. 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:

a • 0 = 0

You might be thinking “That’s OK, but do you really need to do that – plop in letters in place of numbers and stuff?” Well, yes. 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.

The basic purpose of algebra has been the same for thousands of years – to allow people to solve problems with unknown answers.

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. The counting numbers (1, 2, 3, …) are called **natural numbers**. When you are counting people, you wouldn’t count a half person - it wouldn't be **natural**. You can also use natural numbers to make lists.

**Whole numbers** act a lot like the natural numbers. In fact, they are the same except we have added **zero** to the list (0, 1, 2, 3, …).

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 at zero.

Algebra problems often require you to round your answer to the nearest whole number. This makes sense, especially when the problem involves people, cars, houses, or anything that shouldn’t be cut into pieces.

**Integers** broaden your number range a little bit. They allow you to include all whole numbers and their **opposites**.
You can think of integers as being the positive and negative whole numbers (…-3, -2, -1, 0, 1, 2, 3, …). 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 150 miles. When you come home, you can think of it as driving -150 miles (negative 150 miles), the 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). If you get an error statement from your calculator, check the negative/minus signs first.

**Rational** numbers act rationally - they sort of make sense - at least they make sense to math people. Rational numbers are what you get when you divide
integers by integers, so they can be either positive or negative. 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 0.3333 or .25000, is a rational number. 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, ..), zero (0), all the opposites (-1, -2, -3, ..), all fractions (¼, ½, ¾, 2¼) and most (but not all) decimals.

The last type of real numbers are called **irrational**. They are just what you expect from the name – they are the opposite of rational numbers. 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.

**Algebra I Book **- Algebra I published by Glencoe/McGraw Hill, copyright 2005, available on disk or on-line.

**Noteables** - this companion to the textbook will help you to take good notes.

**Foldables** – each chapter uses "Foldables" as a way to help you organize you notes from the chapter.

**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 884) 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 797 with green edges on its pages, this provides a good review of things you should have learned in math before beginning Algebra 1.

**Selected Answers** – beginning on page R17 also has green edges on its pages. 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.

© K. A. Shearer 2005-2010

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