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Introduction to Algebra

Dinakshi Arora
Critical thinking, Problem Solving
Understand, Application

Introduction to Algebra
Define variables, numerical expressions and algebraic expressions.Examine examples in which phrases are translated into algebraic expressions.Examine real-world problems in which phrases are translated into algebraic expressions.Explain the use of different letters to represent a variable.Translate phrases in algebraic expressions. Apply procedures to complete interactive exercises.
When students make the transition from concrete arithmetic to the symbolic language of algebra, they develop abstract reasoning skills necessary to excel in math and science. This concept can easily be explained as Algebra being a way to solve the missing links in a puzzle.
blackboard, chalk, practice sheet handouts

Step 1: What is Algebra?

Don’t be suspicious of the big, heavy word – Algebra. Algebra is just a friend you haven’t made yet.

We all know numbers. We all know what all we can do with numbers. We can add, subtract, multiply and divide them, right? All that is called Arithmetic. Arithmetic is about combining numbers.

Step 2: For example, we can add 3 numbers like






Step 3: We can multiply 2 numbers like


x 16



Step4: We can divide like



Step 5: But do you know we can write all of the above operations horizontally as well? Here we go:


25+36+43 = something

348×16 = something

758/6 = something

Step 6: Now the above problems have become EQUATIONS.

An equation has two sides with an “=” in the middle and ‘something’ in it is unknown, at least till the time we find it.

The equation can be more complex than examples shown above. For instance:

(50+347)/73 = something

Now, Algebra is something that involves equations and here the ‘something’ can be anywhere, not necessarily on the right hand side of ‘=’ and alone. Like:

2 * something – 11 = 9

That is to say, if you double a number and subtract 11 from it, you get 9.

The ‘something’ can be in more than one place too:

2 * something – 7 = something + 3

And you know what, there can be more than one ‘something’s in an equation. But we don’t call them ‘something’, we call them a variable and we treat them as we would treat any other number like 6 or 10. We usually write x, y, z etc. to denote variables. So the above equation will become:


2 * x – 7 = x + 3

A combination of letters (variables) and numbers is called an Algebraic Expression.

An equation is where one expression equals another.  And our job is to find the variable(s).

So basically, algebra is the study of how to handle expressions so we can find the variable(s). That has to be done according to some rules. We’ll learn about those rules as we go along.

Till then, what are the simplest expressions?

Numbers themselves!

Some Practice equations can be given to solve in class.
Can this statement be true?
x+1= 0
Explain why?
Accurate, Clearly explained, Knowledgeable, Precise

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