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5th Grade Order of Operations Guide

Order of Operations PEMDAS Parentheses
πŸ“˜ PEMDAS πŸ“˜ Parentheses πŸ“˜ Operator Precedence πŸ“˜ Brackets

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

5.OA.A.1 Last updated: 2026-05-03

Guide Study Map

What this Order of Operations guide helps students understand

This hub is for students who need free order of operations practice that shows the reasoning, not just the answer. It groups 30 browser-based missions around evaluating expressions in a consistent structure, aligned with 5.OA.A.1.

Mastery Goals

  • Understand evaluating expressions in a consistent structure.
  • Use operation trees, grouping symbols, and step cards before switching to symbolic notation.
  • Explain the answer in words, diagrams, or equations instead of guessing.

Mistakes to Watch

  • Reading left to right even when grouping or multiplication/division should happen first.
  • Skipping the visual model and trying to memorize a procedure for order of operations.
Open practice hub Back to handbook

PEMDAS Hierarchy

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

P E MD AS

Parentheses Change the Answer

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

14 vs 20

The Complete Guide

Order of Operations (PEMDAS): Grade 5 Guide

πŸ“– 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: β€œUse 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 β€œdo 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 β€” that’s their whole point.

πŸ’‘ Steps to Visualize Orderofops: A Thinking Path

Step 1: Concrete Compare

Compute 2 + 3 Γ— 4 (do Γ— first β†’ 2 + 12 = 14). Now compute (2 + 3) Γ— 4 (parens first β†’ 5 Γ— 4 = 20). Why are they different?

Step 2: Pictorial Walk

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

Step 3: Abstract Nesting

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

πŸ–ΌοΈ Common Orderofops Mistakes and How to Fix Them

Visual Model: A vertical PEMDAS ladder: P (parens) at top, E (exponents), MD (Γ—Γ· same level), AS (+βˆ’ same level), with arrows pointing top-to-bottom indicating order.

Pitfall 1: Going strictly left to right ignoring Γ— precedence.

πŸ”§ 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.

πŸ”§ Parent Correction Tip: A and S are equal β€” left to right. M and D are equal β€” left to right. Don’t prefer one over the other.

Pitfall 3: Ignoring nested brackets.

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

πŸ”— What to Learn Next After Orderofops

πŸ‘‰ Start Orderofops Practice Now

  • Expressions (G6) β€” Grade 6 algebraic expressions use the same precedence with variables.
  • Equations (G6) β€” Solving equations requires reversing PEMDAS (SADMEP).

Aligned with CCSS 5.OA.A.1 | Last updated: 2026-05-03