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Grade 5 Order of Operations | Socratic Math

Order of Operations PEMDAS Parentheses
📘 PEMDAS 📘 Parentheses 📘 Operator Precedence 📘 Brackets

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

5.OA.A.1 Last updated: 2026-04-25

PEMDAS Hierarchy

Parentheses → Exponents → Mult/Div (left to right) → Add/Sub (left to right). Same level: left to right.

P E MD AS

Parentheses Change the Answer

2 + 3 × 4 = 14 (× first), but (2 + 3) × 4 = 20 (parens first).

14 vs 20

The Complete Guide

Order of Operations (PEMDAS): Grade 5 Guide

📖 How to Explain Orderofops to Grade 5 Students

Order of operations in Grade 5 codifies what mathematicians have agreed upon. CCSS 5.OA.A.1: “Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.” The acronym PEMDAS (Parens, Exponents, Mult/Div, Add/Sub) prevents the chaos of “do whatever I see first”. Critical nuance: M and D are the same level (left to right); A and S are the same level (left to right). Parentheses can flip an answer entirely — that’s their whole point.

💡 Steps to Visualize Orderofops: A Thinking Path

Step 1: Concrete Compare

Compute 2 + 3 × 4 (do × first → 2 + 12 = 14). Now compute (2 + 3) × 4 (parens first → 5 × 4 = 20). Why are they different?

Step 2: Pictorial Walk

Evaluate 18 - 6 ÷ 2 + 5. Step by step: 6 ÷ 2 = 3 first; then 18 - 3 + 5 left to right = 15 + 5 = 20.

Step 3: Abstract Nesting

Evaluate 4 × [2 + 3 × (6 - 4)]. Innermost parens first: (6-4)=2. Then 3 × 2 = 6. Then 2 + 6 = 8. Then 4 × 8 = 32.

🖼️ Common Orderofops Mistakes and How to Fix Them

Visual Model: A vertical PEMDAS ladder: P (parens) at top, E (exponents), MD (×÷ same level), AS (+− same level), with arrows pointing top-to-bottom indicating order.

Pitfall 1: Going strictly left to right ignoring × precedence.

🔧 Parent Correction Tip: Multiplication and division come BEFORE addition and subtraction, regardless of position.

Pitfall 2: Doing addition before subtraction or multiplication before division when both are present.

🔧 Parent Correction Tip: A and S are equal — left to right. M and D are equal — left to right. Don’t prefer one over the other.

Pitfall 3: Ignoring nested brackets.

🔧 Parent Correction Tip: Always work the INNERMOST grouping first, then work outward layer by layer.

🔗 What to Learn Next After Orderofops

👉 Start Orderofops Practice Now

  • Expressions — Grade 6 algebraic expressions use the same precedence with variables.
  • Equations — Solving equations requires reversing PEMDAS (SADMEP).

Aligned with CCSS 5.OA.A.1 | Last updated: 2026-04-25