Variables and Expressions

Definition

Variables and expressions are fundamental algebraic concepts where letters or symbols represent unknown values, and expressions combine these variables with numbers and operations to represent mathematical relationships.

Prerequisites

To understand variables and expressions, you should have mastered:

Learning Objectives

After mastering variables and expressions, you should be able to:

Understand what variables represent
Write algebraic expressions for word problems
Evaluate expressions with given variable values
Simplify algebraic expressions
Combine like terms in expressions
Use variables to represent patterns
Apply the distributive property

Key Concepts

Variables

Letters representing unknown values
Variables in formulas
Variables in patterns
Domain and range

Algebraic Expressions

Terms
Coefficients
Constants
Like terms
Combining like terms

Properties

Distributive property
Commutative property
Associative property
Identity property

Examples

Example 1: Writing Expressions (Grade 6)

Problem: Write an expression for "three more than twice a number"

Solution: 1. Let x be the number 2. Twice the number is 2x 3. Three more than that is 2x + 3 4. Answer: 2x + 3

Example 2: Evaluating Expressions (Grade 6)

Problem: Evaluate 3x + 2 when x = 4

Solution: 1. Replace x with 4 2. 3(4) + 2 3. 12 + 2 4. Answer: 14

Example 3: Combining Like Terms (Grade 7)

Problem: Simplify 2x + 5 + 3x - 2

Solution: 1. Group like terms: - Terms with x: 2x + 3x - Numbers: 5 - 2 2. Combine like terms: - 2x + 3x = 5x - 5 - 2 = 3 3. Answer: 5x + 3

Common Misconceptions

Thinking variables always represent whole numbers
Confusing multiplication with variables (3x vs. 3 + x)
Not recognizing like terms
Forgetting the distributive property

Progression Path

This skill leads to:

Practice Activities

Basic: Write expressions from words
Intermediate: Evaluate expressions with given values
Advanced: Combine like terms and simplify
Challenge: Use variables to solve word problems