How to Introduce Order of Operations- Teaching PEMDAS Effectively

What You Actually Need to Know About Teaching PEMDAS

Order of operations trips up more students than almost any other math concept. Not because it's hard—because it's taught wrong. Most teachers introduce PEMDAS as a memorization trick instead of a logical system. That approach fails.

This guide skips the fluff and shows you what actually works when students are learning to evaluate expressions correctly.

Why Students Struggle With Order of Operations

The problem isn't the concept. It's how it's presented.

Most textbooks jump straight to "Please Excuse My Dear Aunt Sally" and call it done. Students memorize the letters, then freeze when they see 8 + 2 × 3. Do they add first? Subtract? The acronym becomes meaningless noise.

Here's what actually happens in classrooms:

• Students learn PEMDAS as a chant without understanding what each letter means
• Teachers rush through why the order matters, not just what the order is
• Practice problems jump straight to complex expressions before students grasp basics
• Multiplication and division get taught as separate steps, but students treat them as different operations entirely

The result? Students solve 6 ÷ 2(1 + 2) differently depending on the teacher they ask. That's not a math problem. That's a teaching problem.

The Real Meaning Behind PEMDAS

Before students can use the order of operations, they need to understand why the order exists in the first place.

Math needs a universal language. Without agreed-upon rules, 3 + 4 × 2 could equal 14 or 11 depending on who solved it. PEMDAS guarantees everyone gets the same answer.

Break it down simply:

• Parentheses first — solve anything grouped together
• Exponents next — powers and roots
• Multiplication and Division — left to right
• Addition and Subtraction — left to right

The last two points trip people up constantly. Multiplication doesn't come before division. They're the same priority. Same with addition and subtraction. Work from left to right through each pair.

How to Introduce Order of Operations the Right Way

Step 1: Start With Why

Before writing a single expression, pose a problem. Ask students to solve 5 + 3 × 4. Let them argue. Some will say 32 (adding first). Some will say 17 (multiplying first).

Then show them the problem. No agreed-upon rules means no consistent answers. Math needs consistency. That's why the order exists.

Step 2: Teach Parentheses as Grouping

Start only with parentheses. Give students problems like (5 + 3) × 4 and 5 + (3 × 4). Same numbers, different grouping, different answers.

Get them comfortable with the idea that parentheses override everything. This builds the foundation.

Step 3: Add Exponents

Once parentheses make sense, introduce exponents. 2³ means 2 × 2 × 2. Show that exponents come after parentheses but before everything else.

Step 4: Teach Multiplication and Division as a Pair

This is where most textbooks fail. Students hear "multiplication before division" and never unlearn it.

Use examples that force the point. 8 ÷ 4 × 2 — work left to right. The answer is 4, not 1. If multiplication came first, you'd get 8 ÷ 8 = 1. That's wrong.

Drill this until students stop making the mistake.

Step 5: Same for Addition and Subtraction

10 - 3 + 2 = 9, not 5. Left to right. Always left to right.

Common Mistakes to Watch For

• Treating PEMDAS as a strict top-down checklist instead of a priority system
• Multiplying before dividing (or adding before subtracting) without checking left-to-right
• Solving parentheses incorrectly, then forgetting to distribute or apply results properly
• Skipping steps and making arithmetic errors under pressure
• Ignoring implied multiplication (2(3) means 2 × 3, same priority as explicit ×)

Teaching Approaches Compared

Practice Problems That Actually Teach

Don't give students a worksheet of 30 identical expressions. Vary the problems. Mix these types:

• Two-step expressions: 4 + 6 ÷ 2
• Parentheses first: (4 + 6) ÷ 2
• Nested grouping: 2[(3 + 1) - 1]
• Exponents included: 2 + 3² × 2
• All operations: 8 ÷ 4 + 3 × (2² - 1)

Require students to show every step. No skipping. The goal is building a habit of working systematically, not racing to an answer.

Getting Started: Your First Lesson Plan

Minute 0-5: Pose the consistency problem. Let students argue about a simple expression. Don't resolve it yet.

Minute 5-15: Introduce parentheses as the "override" button. Practice 5-6 problems with only parentheses and basic addition/subtraction.

Minute 15-25: Add multiplication. Show that parentheses still come first. Introduce the full PEMDAS framework—but emphasize left-to-right rules for M/D and A/S.

Minute 25-35: Controlled practice. Walk through 3-4 problems together, narrating every decision out loud. Then have students solve 2-3 independently.

Minute 35-40: Exit ticket. One problem that tests whether they can apply the rules without being reminded of the acronym.

When Students Still Struggle

If a student can't remember the order after several lessons, the problem is usually working memory, not comprehension. They need a reference card—but make them build it themselves. Writing reinforces learning better than reading.

For students who rush, require verbal explanations of each step. If they can't explain why they divided before subtracting, they don't actually understand the process.

What This Comes Down To

PEMDAS isn't a magic chant. It's a logical system that guarantees consistent answers. Teach it as such. Start with the problem of inconsistency, build understanding of each rule, practice with varied problems, and require students to show their work.

Skip the posters. Skip the songs. Skip the inspirational speeches about math being beautiful. Students need clarity, practice, and feedback. That's it.