Grade 6 algebra lesson
Introduction to Algebra: Variables, Expressions, and Simple Examples
Introduction to algebra starts with letters that stand for numbers, then builds expressions, evaluates them with given values, and compares equivalent expressions.
What is algebra?
Algebra is a way to write numbers, patterns, and unknown values with letters.
The letter is not there to make math confusing. It is there so we can talk about a number even when we do not know it yet.
For example, instead of saying "some number plus 5," we can write x + 5.
Variables
A variable is a letter that stands for a number.
Common variables are x, n, a, and p.
Example: If one notebook costs 3 dollars, then 3n can mean the cost of n notebooks.
In algebra, 3n means 3 * n. The multiplication sign is often left out between a number and a letter.
Expressions
An expression is a math phrase. It has numbers, variables, and operations, but no equals sign.
Examples of expressions: x + 7, 4n, 2a + 5, and 3(x + 2).
You can simplify an expression or evaluate it, but you do not "solve" it unless it is part of an equation.
Equations
An equation is a math sentence with an equals sign.
Examples of equations: x + 7 = 15, 4n = 28, and 2a + 5 = 17.
Easy rule: an expression can be evaluated. An equation can be solved.
Terms, coefficients, and constants
A term is one part of an expression. In 3x + 7, the terms are 3x and 7.
A coefficient is the number multiplying the variable. In 3x, the coefficient is 3.
A constant is a number with no variable. In 3x + 7, the constant is 7.
These words help students describe algebra work clearly.
Evaluating expressions
To evaluate an expression, replace the variable with the value you are given, then calculate.
Example: Evaluate x + 7 when x = 9.
Replace x with 9: 9 + 7 = 16.
So the value of x + 7 is 16 when x = 9.
Evaluating with multiplication
Example: Evaluate 3n + 2 when n = 5.
First remember that 3n means 3 * n.
Substitute: 3 * 5 + 2.
Multiply first, then add: 15 + 2 = 17.
Answer: 17.
Equivalent expressions
Equivalent expressions look different but have the same value for every value of the variable.
Example: x + x + x is equivalent to 3x because both mean three groups of x.
Example: 4x + 2x is equivalent to 6x because 4 groups of x plus 2 groups of x makes 6 groups of x.
A simple equation preview
A beginner equation might look like x + 6 = 14.
This means "what number plus 6 makes 14?" The answer is x = 8.
Another beginner equation is 4x = 24. This means "4 times what number makes 24?" The answer is x = 6.
For a full step-by-step guide, continue with Solving Algebra Equations.
Quick beginner tips
Read 3x as "3 times x."
Do not combine unlike terms. 4x + 5 is not 9x.
When evaluating, substitute first and then calculate.
When solving an equation, check the answer by putting it back into the original equation.
Short practice
1. Is x + 5 an expression or an equation?
2. Evaluate 2x + 3 when x = 4.
3. Simplify 5a + 2a.
4. What does 6n mean?
Practice answers
1. x + 5 is an expression because it has no equals sign.
2. 2 * 4 + 3 = 8 + 3 = 11.
3. 5a + 2a = 7a.
4. 6n means 6 * n.