Introduction to Pre-Algebra: Preparing for Middle School Math

What Is Pre-Algebra?

Pre-algebra bridges arithmetic and algebra. It introduces:

Variables (letters representing numbers)
Expressions and equations
Negative numbers
Order of operations
Ratios and proportions

The Big Shift: From Answers to Relationships

In arithmetic: "What is 3 + 5?" In algebra: "If x + 5 = 8, what is x?"

Kids move from finding answers to finding unknowns and understanding relationships.

Variables: Letters as Numbers

Start simple:

"I'm thinking of a number. When I add 3, I get 10. What's my number?"
Answer: 7
As an equation: x + 3 = 10

The variable isn't scary — it's just a mystery number.

Order of Operations (PEMDAS)

The correct order:

Parentheses first
Exponents next
Multiplication and Division (left to right)
Addition and Subtraction (left to right)

Example: 3 + 4 × 2 = ?

Not: 7 × 2 = 14
Yes: 3 + 8 = 11 (multiply first!)

Negative Numbers

Use a number line:

Right = positive
Left = negative
Zero in the middle

Key concepts:

Adding a negative = subtracting
Subtracting a negative = adding
Negative × negative = positive

Solving Simple Equations

The golden rule: What you do to one side, do to the other.

Example: x + 5 = 12

Subtract 5 from both sides
x = 7

Example: 3x = 15

Divide both sides by 3
x = 5

Common Struggles

Sign errors: Losing track of negatives

Solution: Write out every step, be careful

Variable fear: "I don't understand letters in math"

Solution: Start with "mystery number" problems

Order of operations: Forgetting PEMDAS

Solution: Practice, practice, practice

When to Worry

Pre-algebra struggles often stem from gaps in:

Fraction operations
Integer operations (negative numbers)
Basic multiplication/division facts

If your child is lost, check these foundations first.

Practice Resources

Build pre-algebra skills: